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integration</title> <meta name="description" content="Search results for: numerical integration"> <meta name="keywords" content="numerical integration"> <meta name="viewport" content="width=device-width, initial-scale=1, minimum-scale=1, maximum-scale=1, user-scalable=no"> <meta charset="utf-8"> <link href="https://cdn.waset.org/favicon.ico" type="image/x-icon" rel="shortcut icon"> <link href="https://cdn.waset.org/static/plugins/bootstrap-4.2.1/css/bootstrap.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/plugins/fontawesome/css/all.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/css/site.css?v=150220211555" rel="stylesheet"> </head> <body> <header> <div class="container"> <nav class="navbar navbar-expand-lg navbar-light"> <a class="navbar-brand" href="https://waset.org"> <img src="https://cdn.waset.org/static/images/wasetc.png" alt="Open Science Research Excellence" title="Open Science Research Excellence" /> </a> <button class="d-block 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action="https://publications.waset.org/abstracts/search"> <div id="custom-search-input"> <div class="input-group"> <i class="fas fa-search"></i> <input type="text" class="search-query" name="q" placeholder="Author, Title, Abstract, Keywords" value="numerical integration"> <input type="submit" class="btn_search" value="Search"> </div> </div> </form> </div> </div> <div class="row mt-3"> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Commenced</strong> in January 2007</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Frequency:</strong> Monthly</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Edition:</strong> International</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Paper Count:</strong> 6062</div> </div> </div> </div> <h1 class="mt-3 mb-3 text-center" style="font-size:1.6rem;">Search results for: numerical integration</h1> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">6062</span> Improvement of the Numerical Integration's Quality in Meshless Methods</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ahlem%20Mougaida">Ahlem Mougaida</a>, <a href="https://publications.waset.org/abstracts/search?q=Hedi%20Bel%20Hadj%20Salah"> Hedi Bel Hadj Salah</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Several methods are suggested to improve the numerical integration in Galerkin weak form for Meshless methods. In fact, integrating without taking into account the characteristics of the shape functions reproduced by Meshless methods (rational functions, with compact support etc.), causes a large integration error that influences the PDE’s approximate solution. Comparisons between different methods of numerical integration for rational functions are discussed and compared. The algorithms are implemented in Matlab. Finally, numerical results were presented to prove the efficiency of our algorithms in improving results. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=adaptive%20methods" title="adaptive methods">adaptive methods</a>, <a href="https://publications.waset.org/abstracts/search?q=meshless" title=" meshless"> meshless</a>, <a href="https://publications.waset.org/abstracts/search?q=numerical%20integration" title=" numerical integration"> numerical integration</a>, <a href="https://publications.waset.org/abstracts/search?q=rational%20quadrature" title=" rational quadrature"> rational quadrature</a> </p> <a href="https://publications.waset.org/abstracts/46442/improvement-of-the-numerical-integrations-quality-in-meshless-methods" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/46442.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">364</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">6061</span> Development of Fem Code for 2-D Elasticity Problems Using Quadrilateral and Triangular Elements </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Muhammad%20Umar%20Kiani">Muhammad Umar Kiani</a>, <a href="https://publications.waset.org/abstracts/search?q=Waseem%20Sakawat"> Waseem Sakawat</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This study presents the development of FEM code using Quadrilateral 4-Node (Q4) and Triangular 3-Node (T3) elements. Code is formulated using MATLAB language. Instead of using both elements in the same code, two separate codes are written. Quadrilateral element is difficult to handle directly, that is why natural coordinates (eta, ksi) are used. Due to this, Q4 code includes numerical integration (Gauss quadrature). In this case, complete numerical integration is performed using 2 points. On the other hand, T3 element can be modeled directly, by using direct stiffness approach. Axially loaded element, cantilever (special constraints) and Patch test cases were analyzed using both codes and the results were verified by using Ansys. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=FEM%20code" title="FEM code">FEM code</a>, <a href="https://publications.waset.org/abstracts/search?q=MATLAB" title=" MATLAB"> MATLAB</a>, <a href="https://publications.waset.org/abstracts/search?q=numerical%20integration" title=" numerical integration"> numerical integration</a>, <a href="https://publications.waset.org/abstracts/search?q=ANSYS" title=" ANSYS"> ANSYS</a> </p> <a href="https://publications.waset.org/abstracts/2344/development-of-fem-code-for-2-d-elasticity-problems-using-quadrilateral-and-triangular-elements" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/2344.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">418</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">6060</span> A New Family of Integration Methods for Nonlinear Dynamic Analysis</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Shuenn-Yih%20Chang">Shuenn-Yih Chang</a>, <a href="https://publications.waset.org/abstracts/search?q=Chiu-LI%20Huang"> Chiu-LI Huang</a>, <a href="https://publications.waset.org/abstracts/search?q=Ngoc-Cuong%20Tran"> Ngoc-Cuong Tran</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A new family of structure-dependent integration methods, whose coefficients of the difference equation for displacement increment are functions of the initial structural properties and the step size for time integration, is proposed in this work. This family method can simultaneously integrate the controllable numerical dissipation, explicit formulation and unconditional stability together. In general, its numerical dissipation can be continuously controlled by a parameter and it is possible to achieve zero damping. In addition, it can have high-frequency damping to suppress or even remove the spurious oscillations high frequency modes. Whereas, the low frequency modes can be very accurately integrated due to the almost zero damping for these low frequency modes. It is shown herein that the proposed family method can have exactly the same numerical properties as those of HHT-α method for linear elastic systems. In addition, it still preserves the most important property of a structure-dependent integration method, which is an explicit formulation for each time step. Consequently, it can save a huge computational efforts in solving inertial problems when compared to the HHT-α method. In fact, it is revealed by numerical experiments that the CPU time consumed by the proposed family method is only about 1.6% of that consumed by the HHT-α method for the 125-DOF system while it reduces to be 0.16% for the 1000-DOF system. Apparently, the saving of computational efforts is very significant. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=structure-dependent%20integration%20method" title="structure-dependent integration method">structure-dependent integration method</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20dynamic%20analysis" title=" nonlinear dynamic analysis"> nonlinear dynamic analysis</a>, <a href="https://publications.waset.org/abstracts/search?q=unconditional%20stability" title=" unconditional stability"> unconditional stability</a>, <a href="https://publications.waset.org/abstracts/search?q=numerical%20dissipation" title=" numerical dissipation"> numerical dissipation</a>, <a href="https://publications.waset.org/abstracts/search?q=accuracy" title=" accuracy"> accuracy</a> </p> <a href="https://publications.waset.org/abstracts/22306/a-new-family-of-integration-methods-for-nonlinear-dynamic-analysis" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/22306.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">639</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">6059</span> A Family of Second Derivative Methods for Numerical Integration of Stiff Initial Value Problems in Ordinary Differential Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Luke%20Ukpebor">Luke Ukpebor</a>, <a href="https://publications.waset.org/abstracts/search?q=C.%20E.%20Abhulimen"> C. E. Abhulimen</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Stiff initial value problems in ordinary differential equations are problems for which a typical solution is rapidly decaying exponentially, and their numerical investigations are very tedious. Conventional numerical integration solvers cannot cope effectively with stiff problems as they lack adequate stability characteristics. In this article, we developed a new family of four-step second derivative exponentially fitted method of order six for the numerical integration of stiff initial value problem of general first order differential equations. In deriving our method, we employed the idea of breaking down the general multi-derivative multistep method into predator and corrector schemes which possess free parameters that allow for automatic fitting into exponential functions. The stability analysis of the method was discussed and the method was implemented with numerical examples. The result shows that the method is A-stable and competes favorably with existing methods in terms of efficiency and accuracy. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=A-stable" title="A-stable">A-stable</a>, <a href="https://publications.waset.org/abstracts/search?q=exponentially%20fitted" title=" exponentially fitted"> exponentially fitted</a>, <a href="https://publications.waset.org/abstracts/search?q=four%20step" title=" four step"> four step</a>, <a href="https://publications.waset.org/abstracts/search?q=predator-corrector" title=" predator-corrector"> predator-corrector</a>, <a href="https://publications.waset.org/abstracts/search?q=second%20derivative" title=" second derivative"> second derivative</a>, <a href="https://publications.waset.org/abstracts/search?q=stiff%20initial%20value%20problems" title=" stiff initial value problems"> stiff initial value problems</a> </p> <a href="https://publications.waset.org/abstracts/73388/a-family-of-second-derivative-methods-for-numerical-integration-of-stiff-initial-value-problems-in-ordinary-differential-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/73388.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">258</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">6058</span> Using Derivative Free Method to Improve the Error Estimation of Numerical Quadrature</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Chin-Yun%20Chen">Chin-Yun Chen</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Numerical integration is an essential tool for deriving different physical quantities in engineering and science. The effectiveness of a numerical integrator depends on different factors, where the crucial one is the error estimation. This work presents an error estimator that combines a derivative free method to improve the performance of verified numerical quadrature. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=numerical%20quadrature" title="numerical quadrature">numerical quadrature</a>, <a href="https://publications.waset.org/abstracts/search?q=error%20estimation" title=" error estimation"> error estimation</a>, <a href="https://publications.waset.org/abstracts/search?q=derivative%20free%20method" title=" derivative free method"> derivative free method</a>, <a href="https://publications.waset.org/abstracts/search?q=interval%20computation" title=" interval computation "> interval computation </a> </p> <a href="https://publications.waset.org/abstracts/17210/using-derivative-free-method-to-improve-the-error-estimation-of-numerical-quadrature" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/17210.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">463</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">6057</span> Weak Instability in Direct Integration Methods for Structural Dynamics</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Shuenn-Yih%20Chang">Shuenn-Yih Chang</a>, <a href="https://publications.waset.org/abstracts/search?q=Chiu-Li%20Huang"> Chiu-Li Huang</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Three structure-dependent integration methods have been developed for solving equations of motion, which are second-order ordinary differential equations, for structural dynamics and earthquake engineering applications. Although they generally have the same numerical properties, such as explicit formulation, unconditional stability and second-order accuracy, a different performance is found in solving the free vibration response to either linear elastic or nonlinear systems with high frequency modes. The root cause of this different performance in the free vibration responses is analytically explored herein. As a result, it is verified that a weak instability is responsible for the different performance of the integration methods. In general, a weak instability will result in an inaccurate solution or even numerical instability in the free vibration responses of high frequency modes. As a result, a weak instability must be prohibited for time integration methods. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=dynamic%20analysis" title="dynamic analysis">dynamic analysis</a>, <a href="https://publications.waset.org/abstracts/search?q=high%20frequency" title=" high frequency"> high frequency</a>, <a href="https://publications.waset.org/abstracts/search?q=integration%20method" title=" integration method"> integration method</a>, <a href="https://publications.waset.org/abstracts/search?q=overshoot" title=" overshoot"> overshoot</a>, <a href="https://publications.waset.org/abstracts/search?q=weak%20instability" title=" weak instability"> weak instability</a> </p> <a href="https://publications.waset.org/abstracts/107364/weak-instability-in-direct-integration-methods-for-structural-dynamics" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/107364.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">223</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">6056</span> Stable Time Reversed Integration of the Navier-Stokes Equation Using an Adjoint Gradient Method</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Jurriaan%20Gillissen">Jurriaan Gillissen</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This work is concerned with stabilizing the numerical integration of the Navier-Stokes equation (NSE), backwards in time. Applications involve the detection of sources of, e.g., sound, heat, and pollutants. Stable reverse numerical integration of parabolic differential equations is also relevant for image de-blurring. While the literature addresses the reverse integration problem of the advection-diffusion equation, the problem of numerical reverse integration of the NSE has, to our knowledge, not yet been addressed. Owing to the presence of viscosity, the NSE is irreversible, i.e., when going backwards in time, the fluid behaves, as if it had a negative viscosity. As an effect, perturbations from the perfect solution, due to round off errors or discretization errors, grow exponentially in time, and reverse integration of the NSE is inherently unstable, regardless of using an implicit time integration scheme. Consequently, some sort of filtering is required, in order to achieve a stable, numerical, reversed integration. The challenge is to find a filter with a minimal adverse affect on the accuracy of the reversed integration. In the present work, we explore an adjoint gradient method (AGM) to achieve this goal, and we apply this technique to two-dimensional (2D), decaying turbulence. The AGM solves for the initial velocity field u0 at t = 0, that, when integrated forward in time, produces a final velocity field u1 at t = 1, that is as close as is feasibly possible to some specified target field v1. The initial field u0 defines a minimum of a cost-functional J, that measures the distance between u1 and v1. In the minimization procedure, the u0 is updated iteratively along the gradient of J w.r.t. u0, where the gradient is obtained by transporting J backwards in time from t = 1 to t = 0, using the adjoint NSE. The AGM thus effectively replaces the backward integration by multiple forward and backward adjoint integrations. Since the viscosity is negative in the adjoint NSE, each step of the AGM is numerically stable. Nevertheless, when applied to turbulence, the AGM develops instabilities, which limit the backward integration to small times. This is due to the exponential divergence of phase space trajectories in turbulent flow, which produces a multitude of local minima in J, when the integration time is large. As an effect, the AGM may select unphysical, noisy initial conditions. In order to improve this situation, we propose two remedies. First, we replace the integration by a sequence of smaller integrations, i.e., we divide the integration time into segments, where in each segment the target field v1 is taken as the initial field u0 from the previous segment. Second, we add an additional term (regularizer) to J, which is proportional to a high-order Laplacian of u0, and which dampens the gradients of u0. We show that suitable values for the segment size and for the regularizer, allow a stable reverse integration of 2D decaying turbulence, with accurate results for more then O(10) turbulent, integral time scales. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=time%20reversed%20integration" title="time reversed integration">time reversed integration</a>, <a href="https://publications.waset.org/abstracts/search?q=parabolic%20differential%20equations" title=" parabolic differential equations"> parabolic differential equations</a>, <a href="https://publications.waset.org/abstracts/search?q=adjoint%20gradient%20method" title=" adjoint gradient method"> adjoint gradient method</a>, <a href="https://publications.waset.org/abstracts/search?q=two%20dimensional%20turbulence" title=" two dimensional turbulence"> two dimensional turbulence</a> </p> <a href="https://publications.waset.org/abstracts/71170/stable-time-reversed-integration-of-the-navier-stokes-equation-using-an-adjoint-gradient-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/71170.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">224</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">6055</span> A Modified Decoupled Semi-Analytical Approach Based On SBFEM for Solving 2D Elastodynamic Problems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=M.%20Fakharian">M. Fakharian</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20I.%20Khodakarami"> M. I. Khodakarami</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, a new trend for improvement in semi-analytical method based on scale boundaries in order to solve the 2D elastodynamic problems is provided. In this regard, only the boundaries of the problem domain discretization are by specific sub-parametric elements. Mapping functions are uses as a class of higher-order Lagrange polynomials, special shape functions, Gauss-Lobatto -Legendre numerical integration, and the integral form of the weighted residual method, the matrix is diagonal coefficients in the equations of elastodynamic issues. Differences between study conducted and prior research in this paper is in geometry production procedure of the interpolation function and integration of the different is selected. Validity and accuracy of the present method are fully demonstrated through two benchmark problems which are successfully modeled using a few numbers of DOFs. The numerical results agree very well with the analytical solutions and the results from other numerical methods. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=2D%20elastodynamic%20problems" title="2D elastodynamic problems">2D elastodynamic problems</a>, <a href="https://publications.waset.org/abstracts/search?q=lagrange%20polynomials" title=" lagrange polynomials"> lagrange polynomials</a>, <a href="https://publications.waset.org/abstracts/search?q=G-L-Lquadrature" title=" G-L-Lquadrature"> G-L-Lquadrature</a>, <a href="https://publications.waset.org/abstracts/search?q=decoupled%20SBFEM" title=" decoupled SBFEM"> decoupled SBFEM</a> </p> <a href="https://publications.waset.org/abstracts/20245/a-modified-decoupled-semi-analytical-approach-based-on-sbfem-for-solving-2d-elastodynamic-problems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/20245.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">444</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">6054</span> A Class of Third Derivative Four-Step Exponential Fitting Numerical Integrator for Stiff Differential Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Cletus%20Abhulimen">Cletus Abhulimen</a>, <a href="https://publications.waset.org/abstracts/search?q=L.%20A.%20Ukpebor"> L. A. Ukpebor</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we construct a class of four-step third derivative exponential fitting integrator of order six for the numerical integration of stiff initial-value problems of the type: y’= f(x,y); y(x₀) =y₀. The implicit method has free parameters which allow it to be fitted automatically to exponential functions. For the purpose of effective implementation of the proposed method, we adopted the techniques of splitting the method into predictor and corrector schemes. The numerical analysis of the stability of the new method was discussed; the results show that the method is A-stable. Finally, numerical examples are presented, to show the efficiency and accuracy of the new method. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=third%20derivative%20four-step" title="third derivative four-step">third derivative four-step</a>, <a href="https://publications.waset.org/abstracts/search?q=exponentially%20fitted" title=" exponentially fitted"> exponentially fitted</a>, <a href="https://publications.waset.org/abstracts/search?q=a-stable" title=" a-stable"> a-stable</a>, <a href="https://publications.waset.org/abstracts/search?q=stiff%20differential%20equations" title=" stiff differential equations"> stiff differential equations</a> </p> <a href="https://publications.waset.org/abstracts/74060/a-class-of-third-derivative-four-step-exponential-fitting-numerical-integrator-for-stiff-differential-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/74060.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">265</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">6053</span> A Continuous Boundary Value Method of Order 8 for Solving the General Second Order Multipoint Boundary Value Problems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=T.%20A.%20Biala">T. A. Biala</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper deals with the numerical integration of the general second order multipoint boundary value problems. This has been achieved by the development of a continuous linear multistep method (LMM). The continuous LMM is used to construct a main discrete method to be used with some initial and final methods (also obtained from the continuous LMM) so that they form a discrete analogue of the continuous second order boundary value problems. These methods are used as boundary value methods and adapted to cope with the integration of the general second order multipoint boundary value problems. The convergence, the use and the region of absolute stability of the methods are discussed. Several numerical examples are implemented to elucidate our solution process. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=linear%20multistep%20methods" title="linear multistep methods">linear multistep methods</a>, <a href="https://publications.waset.org/abstracts/search?q=boundary%20value%20methods" title=" boundary value methods"> boundary value methods</a>, <a href="https://publications.waset.org/abstracts/search?q=second%20order%20multipoint%20boundary%20value%20problems" title=" second order multipoint boundary value problems"> second order multipoint boundary value problems</a>, <a href="https://publications.waset.org/abstracts/search?q=convergence" title=" convergence"> convergence</a> </p> <a href="https://publications.waset.org/abstracts/50749/a-continuous-boundary-value-method-of-order-8-for-solving-the-general-second-order-multipoint-boundary-value-problems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/50749.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">377</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">6052</span> Numerical Applications of Tikhonov Regularization for the Fourier Multiplier Operators</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Fethi%20Soltani">Fethi Soltani</a>, <a href="https://publications.waset.org/abstracts/search?q=Adel%20Almarashi"> Adel Almarashi</a>, <a href="https://publications.waset.org/abstracts/search?q=Idir%20Mechai"> Idir Mechai</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Tikhonov regularization and reproducing kernels are the most popular approaches to solve ill-posed problems in computational mathematics and applications. And the Fourier multiplier operators are an essential tool to extend some known linear transforms in Euclidean Fourier analysis, as: Weierstrass transform, Poisson integral, Hilbert transform, Riesz transforms, Bochner-Riesz mean operators, partial Fourier integral, Riesz potential, Bessel potential, etc. Using the theory of reproducing kernels, we construct a simple and efficient representations for some class of Fourier multiplier operators Tm on the Paley-Wiener space Hh. In addition, we give an error estimate formula for the approximation and obtain some convergence results as the parameters and the independent variables approaches zero. Furthermore, using numerical quadrature integration rules to compute single and multiple integrals, we give numerical examples and we write explicitly the extremal function and the corresponding Fourier multiplier operators. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=fourier%20multiplier%20operators" title="fourier multiplier operators">fourier multiplier operators</a>, <a href="https://publications.waset.org/abstracts/search?q=Gauss-Kronrod%20method%20of%20integration" title=" Gauss-Kronrod method of integration"> Gauss-Kronrod method of integration</a>, <a href="https://publications.waset.org/abstracts/search?q=Paley-Wiener%20space" title=" Paley-Wiener space"> Paley-Wiener space</a>, <a href="https://publications.waset.org/abstracts/search?q=Tikhonov%20regularization" title=" Tikhonov regularization"> Tikhonov regularization</a> </p> <a href="https://publications.waset.org/abstracts/38538/numerical-applications-of-tikhonov-regularization-for-the-fourier-multiplier-operators" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/38538.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">318</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">6051</span> Integration GIS–SCADA Power Systems to Enclosure Air Dispersion Model </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ibrahim%20Shaker">Ibrahim Shaker</a>, <a href="https://publications.waset.org/abstracts/search?q=Amr%20El%20Hossany"> Amr El Hossany</a>, <a href="https://publications.waset.org/abstracts/search?q=Moustafa%20Osman"> Moustafa Osman</a>, <a href="https://publications.waset.org/abstracts/search?q=Mohamed%20El%20Raey"> Mohamed El Raey</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper will explore integration model between GIS–SCADA system and enclosure quantification model to approach the impact of failure-safe event. There are real demands to identify spatial objects and improve control system performance. Nevertheless, the employed methodology is predicting electro-mechanic operations and corresponding time to environmental incident variations. Open processing, as object systems technology, is presented for integration enclosure database with minimal memory size and computation time via connectivity drivers such as ODBC:JDBC during main stages of GIS–SCADA connection. The function of Geographic Information System is manipulating power distribution in contrast to developing issues. In other ward, GIS-SCADA systems integration will require numerical objects of process to enable system model calibration and estimation demands, determine of past events for analysis and prediction of emergency situations for response training. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=air%20dispersion%20model" title="air dispersion model">air dispersion model</a>, <a href="https://publications.waset.org/abstracts/search?q=environmental%20management" title=" environmental management"> environmental management</a>, <a href="https://publications.waset.org/abstracts/search?q=SCADA%20systems" title=" SCADA systems"> SCADA systems</a>, <a href="https://publications.waset.org/abstracts/search?q=GIS%20system" title=" GIS system"> GIS system</a>, <a href="https://publications.waset.org/abstracts/search?q=integration%20power%20system" title=" integration power system"> integration power system</a> </p> <a href="https://publications.waset.org/abstracts/53013/integration-gis-scada-power-systems-to-enclosure-air-dispersion-model" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/53013.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">368</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">6050</span> Design of a Service-Enabled Dependable Integration Environment</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Fuyang%20Peng">Fuyang Peng</a>, <a href="https://publications.waset.org/abstracts/search?q=Donghong%20Li"> Donghong Li</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The aim of information systems integration is to make all the data sources, applications and business flows integrated into the new environment so that unwanted redundancies are reduced and bottlenecks and mismatches are eliminated. Two issues have to be dealt with to meet such requirements: the software architecture that supports resource integration, and the adaptor development tool that help integration and migration of legacy applications. In this paper, a service-enabled dependable integration environment (SDIE), is presented, which has two key components, i.e., a dependable service integration platform and a legacy application integration tool. For the dependable platform for service integration, the service integration bus, the service management framework, the dependable engine for service composition, and the service registry and discovery components are described. For the legacy application integration tool, its basic organization, functionalities and dependable measures taken are presented. Due to its service-oriented integration model, the light-weight extensible container, the service component combination-oriented p-lattice structure, and other features, SDIE has advantages in openness, flexibility, performance-price ratio and feature support over commercial products, is better than most of the open source integration software in functionality, performance and dependability support. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=application%20integration" title="application integration">application integration</a>, <a href="https://publications.waset.org/abstracts/search?q=dependability" title=" dependability"> dependability</a>, <a href="https://publications.waset.org/abstracts/search?q=legacy" title=" legacy"> legacy</a>, <a href="https://publications.waset.org/abstracts/search?q=SOA" title=" SOA"> SOA</a> </p> <a href="https://publications.waset.org/abstracts/56186/design-of-a-service-enabled-dependable-integration-environment" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/56186.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">360</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">6049</span> The Effect of Supply Chain Integration on Information Sharing</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Khlif%20Hamadi">Khlif Hamadi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Supply chain integration has become a potentially valuable way of securing shared information and improving supply chain performance since competition is no longer between organizations but among supply chains. This research conceptualizes and develops three dimensions of supply chain integration (integration with customers, integration with suppliers, and the interorganizational integration) and tests the relationships between supply chain integration, information sharing, and supply chain performance. Furthermore, the four types of information sharing namely; information sharing with customers, information sharing with suppliers, inter-functional information sharing, and intra-organizational information sharing; and the four constructs of Supply Chain Performance represents expenses of costs, asset utilization, supply chain reliability, and supply chain flexibility and responsiveness. The theoretical and practical implications of the study, as well as directions for future research, are discussed. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=supply%20chain%20integration" title="supply chain integration">supply chain integration</a>, <a href="https://publications.waset.org/abstracts/search?q=supply%20chain%20management" title=" supply chain management"> supply chain management</a>, <a href="https://publications.waset.org/abstracts/search?q=information%20sharing" title=" information sharing"> information sharing</a>, <a href="https://publications.waset.org/abstracts/search?q=supply%20chain%20performance" title=" supply chain performance"> supply chain performance</a> </p> <a href="https://publications.waset.org/abstracts/90589/the-effect-of-supply-chain-integration-on-information-sharing" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/90589.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">260</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">6048</span> Robust Numerical Method for Singularly Perturbed Semilinear Boundary Value Problem with Nonlocal Boundary Condition</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Habtamu%20Garoma%20Debela">Habtamu Garoma Debela</a>, <a href="https://publications.waset.org/abstracts/search?q=Gemechis%20File%20Duressa"> Gemechis File Duressa</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this work, our primary interest is to provide ε-uniformly convergent numerical techniques for solving singularly perturbed semilinear boundary value problems with non-local boundary condition. These singular perturbation problems are described by differential equations in which the highest-order derivative is multiplied by an arbitrarily small parameter ε (say) known as singular perturbation parameter. This leads to the existence of boundary layers, which are basically narrow regions in the neighborhood of the boundary of the domain, where the gradient of the solution becomes steep as the perturbation parameter tends to zero. Due to the appearance of the layer phenomena, it is a challenging task to provide ε-uniform numerical methods. The term 'ε-uniform' refers to identify those numerical methods in which the approximate solution converges to the corresponding exact solution (measured to the supremum norm) independently with respect to the perturbation parameter ε. Thus, the purpose of this work is to develop, analyze, and improve the ε-uniform numerical methods for solving singularly perturbed problems. These methods are based on nonstandard fitted finite difference method. The basic idea behind the fitted operator, finite difference method, is to replace the denominator functions of the classical derivatives with positive functions derived in such a way that they capture some notable properties of the governing differential equation. A uniformly convergent numerical method is constructed via nonstandard fitted operator numerical method and numerical integration methods to solve the problem. The non-local boundary condition is treated using numerical integration techniques. Additionally, Richardson extrapolation technique, which improves the first-order accuracy of the standard scheme to second-order convergence, is applied for singularly perturbed convection-diffusion problems using the proposed numerical method. Maximum absolute errors and rates of convergence for different values of perturbation parameter and mesh sizes are tabulated for the numerical example considered. The method is shown to be ε-uniformly convergent. Finally, extensive numerical experiments are conducted which support all of our theoretical findings. A concise conclusion is provided at the end of this work. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=nonlocal%20boundary%20condition" title="nonlocal boundary condition">nonlocal boundary condition</a>, <a href="https://publications.waset.org/abstracts/search?q=nonstandard%20fitted%20operator" title=" nonstandard fitted operator"> nonstandard fitted operator</a>, <a href="https://publications.waset.org/abstracts/search?q=semilinear%20problem" title=" semilinear problem"> semilinear problem</a>, <a href="https://publications.waset.org/abstracts/search?q=singular%20perturbation" title=" singular perturbation"> singular perturbation</a>, <a href="https://publications.waset.org/abstracts/search?q=uniformly%20convergent" title=" uniformly convergent"> uniformly convergent</a> </p> <a href="https://publications.waset.org/abstracts/130967/robust-numerical-method-for-singularly-perturbed-semilinear-boundary-value-problem-with-nonlocal-boundary-condition" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/130967.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">143</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">6047</span> Analyzing the Technology Affecting on the Social Integration of Students at University</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Sujit%20K.%20Basak">Sujit K. Basak</a>, <a href="https://publications.waset.org/abstracts/search?q=Simon%20Collin"> Simon Collin</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The aim of this paper is to examine the technology access and use on the affecting social integration of local students at university. This aim is achieved by designing a structural equation modeling (SEM) in terms of integration with peers, integration with faculty, faculty support and on the other hand, examining the socio demographic impact on the technology access and use. The collected data were analyzed using the WarpPLS 5.0 software. This study was survey based and it was conducted at a public university in Canada. The results of the study indicated that technology has a strong impact on integration with faculty, faculty support, but technology does not have an impact on integration with peers. However, the social demographic has also an impact on the technology access and use. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=faculty" title="faculty">faculty</a>, <a href="https://publications.waset.org/abstracts/search?q=integration" title=" integration"> integration</a>, <a href="https://publications.waset.org/abstracts/search?q=peer" title=" peer"> peer</a>, <a href="https://publications.waset.org/abstracts/search?q=technology%20access%20and%20use" title=" technology access and use"> technology access and use</a> </p> <a href="https://publications.waset.org/abstracts/47248/analyzing-the-technology-affecting-on-the-social-integration-of-students-at-university" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/47248.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">512</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">6046</span> Optimization of the Numerical Fracture Mechanics</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=H.%20Hentati">H. Hentati</a>, <a href="https://publications.waset.org/abstracts/search?q=R.%20Abdelmoula"> R. Abdelmoula</a>, <a href="https://publications.waset.org/abstracts/search?q=Li%20Jia"> Li Jia</a>, <a href="https://publications.waset.org/abstracts/search?q=A.%20Maalej"> A. Maalej</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this work, we present numerical simulations of the quasi-static crack propagation based on the variation approach. We perform numerical simulations of a piece of brittle material without initial crack. An alternate minimization algorithm is used. Based on these numerical results, we determine the influence of numerical parameters on the location of crack. We show the importance of trying to optimize the time of numerical computation and we present the first attempt to develop a simple numerical method to optimize this time. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=fracture%20mechanics" title="fracture mechanics">fracture mechanics</a>, <a href="https://publications.waset.org/abstracts/search?q=optimization" title=" optimization"> optimization</a>, <a href="https://publications.waset.org/abstracts/search?q=variation%20approach" title=" variation approach"> variation approach</a>, <a href="https://publications.waset.org/abstracts/search?q=mechanic" title=" mechanic"> mechanic</a> </p> <a href="https://publications.waset.org/abstracts/5187/optimization-of-the-numerical-fracture-mechanics" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/5187.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">606</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">6045</span> Finite Element Analysis for Earing Prediction Incorporating the BBC2003 Material Model with Fully Implicit Integration Method: Derivation and Numerical Algorithm</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Sajjad%20Izadpanah">Sajjad Izadpanah</a>, <a href="https://publications.waset.org/abstracts/search?q=Seyed%20Hadi%20Ghaderi"> Seyed Hadi Ghaderi</a>, <a href="https://publications.waset.org/abstracts/search?q=Morteza%20Sayah%20Irani"> Morteza Sayah Irani</a>, <a href="https://publications.waset.org/abstracts/search?q=Mahdi%20Gerdooei"> Mahdi Gerdooei</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this research work, a sophisticated yield criterion known as BBC2003, capable of describing planar anisotropic behaviors of aluminum alloy sheets, was integrated into the commercial finite element code ABAQUS/Standard via a user subroutine. The complete formulation of the implementation process using a fully implicit integration scheme, i.e., the classic backward Euler method, is presented, and relevant aspects of the yield criterion are introduced. In order to solve nonlinear differential and algebraic equations, the line-search algorithm was adopted in the user-defined material subroutine (UMAT) to expand the convergence domain of the iterative Newton-Raphson method. The developed subroutine was used to simulate a challenging computational problem with complex stress states, i.e., deep drawing of an anisotropic aluminum alloy AA3105. The accuracy and stability of the developed subroutine were confirmed by comparing the numerically predicted earing and thickness variation profiles with the experimental results, which showed an excellent agreement between numerical and experimental earing and thickness profiles. The integration of the BBC2003 yield criterion into ABAQUS/Standard represents a significant contribution to the field of computational mechanics and provides a useful tool for analyzing the mechanical behavior of anisotropic materials subjected to complex loading conditions. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=BBC2003%20yield%20function" title="BBC2003 yield function">BBC2003 yield function</a>, <a href="https://publications.waset.org/abstracts/search?q=plastic%20anisotropy" title=" plastic anisotropy"> plastic anisotropy</a>, <a href="https://publications.waset.org/abstracts/search?q=fully%20implicit%20integration%20scheme" title=" fully implicit integration scheme"> fully implicit integration scheme</a>, <a href="https://publications.waset.org/abstracts/search?q=line%20search%20algorithm" title=" line search algorithm"> line search algorithm</a>, <a href="https://publications.waset.org/abstracts/search?q=explicit%20and%20implicit%20integration%20schemes" title=" explicit and implicit integration schemes"> explicit and implicit integration schemes</a> </p> <a href="https://publications.waset.org/abstracts/166034/finite-element-analysis-for-earing-prediction-incorporating-the-bbc2003-material-model-with-fully-implicit-integration-method-derivation-and-numerical-algorithm" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/166034.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">75</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">6044</span> Rules in Policy Integration, Case Study: Victoria Catchment Management</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ratri%20Werdiningtyas">Ratri Werdiningtyas</a>, <a href="https://publications.waset.org/abstracts/search?q=Yongping%20Wei"> Yongping Wei</a>, <a href="https://publications.waset.org/abstracts/search?q=Andrew%20Western"> Andrew Western</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper contributes to on-going attempts at bringing together land, water and environmental policy in catchment management. A tension remains in defining the boundaries of policy integration. Most of Integrated Water Resource Management is valued as rhetoric policy. It is far from being achieved on the ground because the socio-ecological system has not been understood and developed into complete and coherent problem representation. To clarify the feature of integration, this article draws on institutional fit for public policy integration and uses these insights in an empirical setting to identify the mechanism that can facilitate effective public integration for catchment management. This research is based on the journey of Victoria’s government from 1890-2016. A total of 274 Victorian Acts related to land, water, environment management published in those periods has been investigated. Four conditions of integration have been identified in their co-evolution: (1) the integration policy based on reserves, (2) the integration policy based on authority interest, (3) policy based on integrated information and, (4) policy based coordinated resource, authority and information. Results suggest that policy coordination among their policy instrument is superior rather than policy integration in the case of catchment management. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=catchment%20management" title="catchment management">catchment management</a>, <a href="https://publications.waset.org/abstracts/search?q=co-evolution" title=" co-evolution"> co-evolution</a>, <a href="https://publications.waset.org/abstracts/search?q=policy%20integration" title=" policy integration"> policy integration</a>, <a href="https://publications.waset.org/abstracts/search?q=phase" title=" phase"> phase</a> </p> <a href="https://publications.waset.org/abstracts/101538/rules-in-policy-integration-case-study-victoria-catchment-management" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/101538.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">247</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">6043</span> Approximations of Fractional Derivatives and Its Applications in Solving Non-Linear Fractional Variational Problems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Harendra%20Singh">Harendra Singh</a>, <a href="https://publications.waset.org/abstracts/search?q=Rajesh%20Pandey"> Rajesh Pandey</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The paper presents a numerical method based on operational matrix of integration and Ryleigh method for the solution of a class of non-linear fractional variational problems (NLFVPs). Chebyshev first kind polynomials are used for the construction of operational matrix. Using operational matrix and Ryleigh method the NLFVP is converted into a system of non-linear algebraic equations, and solving these equations we obtained approximate solution for NLFVPs. Convergence analysis of the proposed method is provided. Numerical experiment is done to show the applicability of the proposed numerical method. The obtained numerical results are compared with exact solution and solution obtained from Chebyshev third kind. Further the results are shown graphically for different fractional order involved in the problems. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=non-linear%20fractional%20variational%20problems" title="non-linear fractional variational problems">non-linear fractional variational problems</a>, <a href="https://publications.waset.org/abstracts/search?q=Rayleigh-Ritz%20method" title=" Rayleigh-Ritz method"> Rayleigh-Ritz method</a>, <a href="https://publications.waset.org/abstracts/search?q=convergence%20analysis" title=" convergence analysis"> convergence analysis</a>, <a href="https://publications.waset.org/abstracts/search?q=error%20analysis" title=" error analysis"> error analysis</a> </p> <a href="https://publications.waset.org/abstracts/57497/approximations-of-fractional-derivatives-and-its-applications-in-solving-non-linear-fractional-variational-problems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/57497.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">298</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">6042</span> Calculate Consumer Surplus and Producer Surplus Using Integration</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Bojan%20Radisic">Bojan Radisic</a>, <a href="https://publications.waset.org/abstracts/search?q=Katarina%20Stavlic"> Katarina Stavlic</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The paper describes two economics terms consumer surplus and producer surplus using the definite integrals (the Riemann integral). The consumer surplus is the difference between what consumers are willing to pay and actual price. The producer surplus is the difference between what producers selling at the current price, rather than at the price they would have been are willing to accept. Using the definite integrals describe terms and mathematical formulas of the consumer surplus and the producer surplus and will be applied to the numerical examples. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=consumer%20surplus" title="consumer surplus">consumer surplus</a>, <a href="https://publications.waset.org/abstracts/search?q=producer%20surplus" title=" producer surplus"> producer surplus</a>, <a href="https://publications.waset.org/abstracts/search?q=definite%20integral" title=" definite integral"> definite integral</a>, <a href="https://publications.waset.org/abstracts/search?q=integration" title=" integration"> integration</a> </p> <a href="https://publications.waset.org/abstracts/29101/calculate-consumer-surplus-and-producer-surplus-using-integration" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/29101.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">587</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">6041</span> Numerical Method for Heat Transfer Problem in a Block Having an Interface</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Beghdadi%20Lotfi">Beghdadi Lotfi</a>, <a href="https://publications.waset.org/abstracts/search?q=Bouziane%20Abdelhafid"> Bouziane Abdelhafid</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A finite volume method for quadrilaterals unstructured mesh is developed to predict the two dimensional steady-state solutions of conduction equation. In this scheme, based on the integration around the polygonal control volume, the derivatives of conduction equation must be converted into closed line integrals using same formulation of the Stokes theorem. To valid the accuracy of the method two numerical experiments s are used: conduction in a regular block (with known analytical solution) and conduction in a rotated block (case with curved boundaries).The numerical results show good agreement with analytical results. To demonstrate the accuracy of the method, the absolute and root-mean square errors versus the grid size are examined quantitatively. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Stokes%20theorem" title="Stokes theorem">Stokes theorem</a>, <a href="https://publications.waset.org/abstracts/search?q=unstructured%20grid" title=" unstructured grid"> unstructured grid</a>, <a href="https://publications.waset.org/abstracts/search?q=heat%20transfer" title=" heat transfer"> heat transfer</a>, <a href="https://publications.waset.org/abstracts/search?q=complex%20geometry" title=" complex geometry"> complex geometry</a> </p> <a href="https://publications.waset.org/abstracts/45081/numerical-method-for-heat-transfer-problem-in-a-block-having-an-interface" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/45081.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">290</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">6040</span> Numerical Solutions of Fractional Order Epidemic Model</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Sadia%20Arshad">Sadia Arshad</a>, <a href="https://publications.waset.org/abstracts/search?q=Ayesha%20Sohail"> Ayesha Sohail</a>, <a href="https://publications.waset.org/abstracts/search?q=Sana%20Javed"> Sana Javed</a>, <a href="https://publications.waset.org/abstracts/search?q=Khadija%20Maqbool"> Khadija Maqbool</a>, <a href="https://publications.waset.org/abstracts/search?q=Salma%20Kanwal"> Salma Kanwal</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The dynamical study of the carriers play an essential role in the evolution and global transmission of infectious diseases and will be discussed in this study. To make this approach novel, we will consider the fractional order model which is generalization of integer order derivative to an arbitrary number. Since the integration involved is non local therefore this property of fractional operator is very useful to study epidemic model for infectious diseases. An extended numerical method (ODE solver) is implemented on the model equations and we will present the simulations of the model for diﬀerent values of fractional order to study the eﬀect of carriers on transmission dynamics. Global dynamics of fractional model are established by using the reproduction number. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Fractional%20di%EF%AC%80erential%20equation" title="Fractional diﬀerential equation">Fractional diﬀerential equation</a>, <a href="https://publications.waset.org/abstracts/search?q=Numerical%20simulations" title=" Numerical simulations"> Numerical simulations</a>, <a href="https://publications.waset.org/abstracts/search?q=epidemic%20model" title=" epidemic model"> epidemic model</a>, <a href="https://publications.waset.org/abstracts/search?q=transmission%20dynamics" title=" transmission dynamics"> transmission dynamics</a> </p> <a href="https://publications.waset.org/abstracts/17447/numerical-solutions-of-fractional-order-epidemic-model" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/17447.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">600</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">6039</span> Characterization and Predictors of Community Integration of People with Psychiatric Problems: Comparisons with the General Population</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=J.%20Cabral">J. Cabral</a>, <a href="https://publications.waset.org/abstracts/search?q=C.%20Barreto%20Carvalho"> C. Barreto Carvalho</a>, <a href="https://publications.waset.org/abstracts/search?q=C.%20da%20Motta"> C. da Motta</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20Sousa"> M. Sousa</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Community integration is a construct that an increasing body of research has shown to have a significant impact in well-being and recovery of people with psychiatric problems. However, there are few studies that explore which factors can be associated and predict community integration. Moreover, community integration has been mostly studied in minority groups, and currently literature on the definition and manifestation of community integration in the more general population is scarce. Thus, the current study aims to characterize community integration and explore possible predictor variables in a sample of participants with psychiatric problems (PP, N=183) and a sample of participants from the general population (GP, N=211). Results show that people with psychiatric problems present above average values of community integration, but are significantly lower than their healthy counterparts. It was also possible to observe that community integration does not vary in terms of the socio-demographic characteristics of both groups in this study. Correlation and multiple regression showed that, among several variables that literature present as relevant in the community integration process, only three variables emerged as having the most explanatory value in community integration of both groups: sense of community, basic needs satisfaction and submission. These results also shown that those variables have increased explanatory power in the PP sample, which leads us to emphasize the need to address this issue in future studies and increase the understanding of the factors that can be involved in the promotion of community integration, in order to devise more effective interventions in this field. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=community%20integration" title="community integration">community integration</a>, <a href="https://publications.waset.org/abstracts/search?q=mental%20illness" title=" mental illness"> mental illness</a>, <a href="https://publications.waset.org/abstracts/search?q=predictors" title=" predictors"> predictors</a>, <a href="https://publications.waset.org/abstracts/search?q=psychiatric%20problems" title=" psychiatric problems"> psychiatric problems</a> </p> <a href="https://publications.waset.org/abstracts/29436/characterization-and-predictors-of-community-integration-of-people-with-psychiatric-problems-comparisons-with-the-general-population" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/29436.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">487</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">6038</span> Comparative Regionalism: The Case of Financial Integration in Association of Southeast Asian Nations </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Sharon%20Kun-Amornpong">Sharon Kun-Amornpong</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, ASEAN financial integration will be discussed from the perspective of the rule of law. The methodology of the paper is comparative regionalism. It will compare the role of the rule of law in ASEAN financial integration with that of the European Union with particular focuses on, for example, institutions and values. The paper argues that in the realm of financial integration, the rule of law is one of the most important factors that could help strengthen and promote financial integration in ASEAN. This is despite the fact that the ‘ASEAN Way’ emphasises non-interference and utilises a consensus-based cooperation rather than formal institutions. Nevertheless, the rule of law for ASEAN financial integration should be situated in its own historical, cultural, and political contexts. In addition, in the case of ASEAN, the rule of law cannot take root if it does not come from the demand of the people in this region. For instance, a reform or creation of legal institutions should not be imposed by international financial institutions. The paper will conclude that law has a normative force. It could shape expectation of market participants and promote deeper financial integration if norms that the law generates have become a significant norm in the society or industry. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Association%20of%20Southeast%20Asian%20Nations" title="Association of Southeast Asian Nations">Association of Southeast Asian Nations</a>, <a href="https://publications.waset.org/abstracts/search?q=ASEAN" title=" ASEAN"> ASEAN</a>, <a href="https://publications.waset.org/abstracts/search?q=comparative%20regionalism" title=" comparative regionalism"> comparative regionalism</a>, <a href="https://publications.waset.org/abstracts/search?q=financial%20integration" title=" financial integration"> financial integration</a>, <a href="https://publications.waset.org/abstracts/search?q=the%20rule%20of%20law" title=" the rule of law"> the rule of law</a> </p> <a href="https://publications.waset.org/abstracts/115999/comparative-regionalism-the-case-of-financial-integration-in-association-of-southeast-asian-nations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/115999.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">208</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">6037</span> Clinch Process Simulation Using Diffuse Elements</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Benzegaou%20Ali">Benzegaou Ali</a>, <a href="https://publications.waset.org/abstracts/search?q=Brani%20Benabderrahmane"> Brani Benabderrahmane</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This work describes a numerical study of the TOX–clinching process using diffuse elements. A computer code baptized SEMA "Static Explicit Method Analysis" is developed to simulate the clinch joining process. The FE code is based on an Updated Lagrangian scheme. The used resolution method is based on an explicit static approach. The integration of the elasto-plastic behavior law is realized with an algorithm of Simo and Taylor. The tools are represented by plane facets. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=diffuse%20elements" title="diffuse elements">diffuse elements</a>, <a href="https://publications.waset.org/abstracts/search?q=numerical%20simulation" title=" numerical simulation"> numerical simulation</a>, <a href="https://publications.waset.org/abstracts/search?q=clinching" title=" clinching"> clinching</a>, <a href="https://publications.waset.org/abstracts/search?q=contact" title=" contact"> contact</a>, <a href="https://publications.waset.org/abstracts/search?q=large%20deformation" title=" large deformation"> large deformation</a> </p> <a href="https://publications.waset.org/abstracts/2241/clinch-process-simulation-using-diffuse-elements" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/2241.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">363</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">6036</span> Investigation of Different Conditions to Detect Cycles in Linearly Implicit Quantized State Systems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Elmongi%20Elbellili">Elmongi Elbellili</a>, <a href="https://publications.waset.org/abstracts/search?q=Ben%20Lauwens"> Ben Lauwens</a>, <a href="https://publications.waset.org/abstracts/search?q=Daan%20Huybrechs"> Daan Huybrechs</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The increasing complexity of modern engineering systems presents a challenge to the digital simulation of these systems which usually can be represented by differential equations. The Linearly Implicit Quantized State System (LIQSS) offers an alternative approach to traditional numerical integration techniques for solving Ordinary Differential Equations (ODEs). This method proved effective for handling discontinuous and large stiff systems. However, the inherent discrete nature of LIQSS may introduce oscillations that result in unnecessary computational steps. The current oscillation detection mechanism relies on a condition that checks the significance of the derivatives, but it could be further improved. This paper describes a different cycle detection mechanism and presents the outcomes using LIQSS order one in simulating the Advection Diffusion problem. The efficiency of this new cycle detection mechanism is verified by comparing the performance of the current solver against the new version as well as a reference solution using a Runge-Kutta method of order14. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=numerical%20integration" title="numerical integration">numerical integration</a>, <a href="https://publications.waset.org/abstracts/search?q=quantized%20state%20systems" title=" quantized state systems"> quantized state systems</a>, <a href="https://publications.waset.org/abstracts/search?q=ordinary%20differential%20equations" title=" ordinary differential equations"> ordinary differential equations</a>, <a href="https://publications.waset.org/abstracts/search?q=stiffness" title=" stiffness"> stiffness</a>, <a href="https://publications.waset.org/abstracts/search?q=cycle%20detection" title=" cycle detection"> cycle detection</a>, <a href="https://publications.waset.org/abstracts/search?q=simulation" title=" simulation"> simulation</a> </p> <a href="https://publications.waset.org/abstracts/182700/investigation-of-different-conditions-to-detect-cycles-in-linearly-implicit-quantized-state-systems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/182700.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">60</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">6035</span> Some Results on the Generalized Higher Rank Numerical Ranges</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mohsen%20Zahraei">Mohsen Zahraei</a> </p> <p class="card-text"><strong>Abstract:</strong></p> ‎In this paper, ‎the notion of ‎rank-k numerical range of rectangular complex matrix polynomials‎ ‎are introduced. ‎Some algebraic and geometrical properties are investigated. ‎Moreover, ‎for ε>0 the notion of Birkhoff-James approximate orthogonality sets for ε-higher ‎rank numerical ranges of rectangular matrix polynomials is also introduced and studied. ‎The proposed definitions yield a natural generalization of the standard higher rank numerical ranges. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=%E2%80%8E%E2%80%8ERank-k%20numerical%20range%E2%80%8E" title="‎‎Rank-k numerical range‎">‎‎Rank-k numerical range‎</a>, <a href="https://publications.waset.org/abstracts/search?q=%E2%80%8Eisometry%E2%80%8E" title=" ‎isometry‎"> ‎isometry‎</a>, <a href="https://publications.waset.org/abstracts/search?q=%E2%80%8Enumerical%20range%E2%80%8E" title=" ‎numerical range‎"> ‎numerical range‎</a>, <a href="https://publications.waset.org/abstracts/search?q=%E2%80%8Erectangular%20matrix%20polynomials" title=" ‎rectangular matrix polynomials"> ‎rectangular matrix polynomials</a> </p> <a href="https://publications.waset.org/abstracts/28955/some-results-on-the-generalized-higher-rank-numerical-ranges" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/28955.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">459</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">6034</span> Data Integration with Geographic Information System Tools for Rural Environmental Monitoring</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Tamas%20Jancso">Tamas Jancso</a>, <a href="https://publications.waset.org/abstracts/search?q=Andrea%20Podor"> Andrea Podor</a>, <a href="https://publications.waset.org/abstracts/search?q=Eva%20Nagyne%20Hajnal"> Eva Nagyne Hajnal</a>, <a href="https://publications.waset.org/abstracts/search?q=Peter%20Udvardy"> Peter Udvardy</a>, <a href="https://publications.waset.org/abstracts/search?q=Gabor%20Nagy"> Gabor Nagy</a>, <a href="https://publications.waset.org/abstracts/search?q=Attila%20Varga"> Attila Varga</a>, <a href="https://publications.waset.org/abstracts/search?q=Meng%20Qingyan"> Meng Qingyan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The paper deals with the conditions and circumstances of integration of remotely sensed data for rural environmental monitoring purposes. The main task is to make decisions during the integration process when we have data sources with different resolution, location, spectral channels, and dimension. In order to have exact knowledge about the integration and data fusion possibilities, it is necessary to know the properties (metadata) that characterize the data. The paper explains the joining of these data sources using their attribute data through a sample project. The resulted product will be used for rural environmental analysis. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=remote%20sensing" title="remote sensing">remote sensing</a>, <a href="https://publications.waset.org/abstracts/search?q=GIS" title=" GIS"> GIS</a>, <a href="https://publications.waset.org/abstracts/search?q=metadata" title=" metadata"> metadata</a>, <a href="https://publications.waset.org/abstracts/search?q=integration" title=" integration"> integration</a>, <a href="https://publications.waset.org/abstracts/search?q=environmental%20analysis" title=" environmental analysis"> environmental analysis</a> </p> <a href="https://publications.waset.org/abstracts/151549/data-integration-with-geographic-information-system-tools-for-rural-environmental-monitoring" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/151549.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">120</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">6033</span> Applying Systems Thinking and a System of Systems Approach to Facilitate Sustainable Grid Integration of Variable Renewable Energy</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Edward%20B.%20Ssekulima">Edward B. Ssekulima</a>, <a href="https://publications.waset.org/abstracts/search?q=Amir%20Etemadi"> Amir Etemadi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper presents a Systems Thinking and System of Systems (SoS) viewpoint for managing requirements complexity in the grid integration of Variable Renewable Energy (VRE). To achieve a SoS approach, it is often necessary to inculcate a Systems Thinking (ST) perspective in the planning and design of the attendant system. We show how this approach can support the enhanced integration of VRE (wind, solar small hydro) for which intermittency is a key inhibiting factor to their sustainable grid integration. The results indicate that a ST and SoS approach are a critical tool for decision makers in the planning, design and deployment of VRE Sources for their sustainable grid-integration in accordance with relevant techno-economic, social and environmental requirements. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=sustainable%20grid-integration" title="sustainable grid-integration">sustainable grid-integration</a>, <a href="https://publications.waset.org/abstracts/search?q=system%20of%20systems" title=" system of systems"> system of systems</a>, <a href="https://publications.waset.org/abstracts/search?q=systems%20thinking" title=" systems thinking"> systems thinking</a>, <a href="https://publications.waset.org/abstracts/search?q=variable%20energy%20resources" title=" variable energy resources"> variable energy resources</a> </p> <a href="https://publications.waset.org/abstracts/158837/applying-systems-thinking-and-a-system-of-systems-approach-to-facilitate-sustainable-grid-integration-of-variable-renewable-energy" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/158837.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">124</span> </span> </div> </div> <ul class="pagination"> <li class="page-item disabled"><span class="page-link">&lsaquo;</span></li> <li class="page-item active"><span class="page-link">1</span></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=numerical%20integration&page=2">2</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=numerical%20integration&page=3">3</a></li> <li class="page-item"><a class="page-link" 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