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method</title> <meta name="description" content="Search results for: collocation method"> <meta name="keywords" content="collocation method"> <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 d-lg-none 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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="collocation method"> <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> 18955</div> </div> </div> </div> <h1 class="mt-3 mb-3 text-center" style="font-size:1.6rem;">Search results for: collocation method</h1> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">18955</span> Numerical Wave Solutions for Nonlinear Coupled Equations Using Sinc-Collocation Method</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Kamel%20Al-Khaled">Kamel Al-Khaled</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, numerical solutions for the nonlinear coupled Korteweg-de Vries, (abbreviated as KdV) equations are calculated by Sinc-collocation method. This approach is based on a global collocation method using Sinc basis functions. First, discretizing time derivative of the KdV equations by a classic finite difference formula, while the space derivatives are approximated by a $\theta-$weighted scheme. Sinc functions are used to solve these two equations. Soliton solutions are constructed to show the nature of the solution. The numerical results are shown to demonstrate the efficiency of the newly proposed method. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Nonlinear%20coupled%20KdV%20equations" title="Nonlinear coupled KdV equations">Nonlinear coupled KdV equations</a>, <a href="https://publications.waset.org/abstracts/search?q=Soliton%20solutions" title=" Soliton solutions"> Soliton solutions</a>, <a href="https://publications.waset.org/abstracts/search?q=Sinc-collocation%20method" title=" Sinc-collocation method"> Sinc-collocation method</a>, <a href="https://publications.waset.org/abstracts/search?q=Sinc%20functions" title=" Sinc functions"> Sinc functions</a> </p> <a href="https://publications.waset.org/abstracts/23564/numerical-wave-solutions-for-nonlinear-coupled-equations-using-sinc-collocation-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/23564.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">524</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">18954</span> Collocation Method Using Quartic B-Splines for Solving the Modified RLW Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=A.%20A.%20Soliman">A. A. Soliman</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The Modified Regularized Long Wave (MRLW) equation is solved numerically by giving a new algorithm based on collocation method using quartic B-splines at the mid-knot points as element shape. Also, we use the fourth Runge-Kutta method for solving the system of first order ordinary differential equations instead of finite difference method. Our test problems, including the migration and interaction of solitary waves, are used to validate the algorithm which is found to be accurate and efficient. The three invariants of the motion are evaluated to determine the conservation properties of the algorithm. The temporal evaluation of a Maxwellian initial pulse is then studied. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=collocation%20method" title="collocation method">collocation method</a>, <a href="https://publications.waset.org/abstracts/search?q=MRLW%20equation" title=" MRLW equation"> MRLW equation</a>, <a href="https://publications.waset.org/abstracts/search?q=Quartic%20B-splines" title=" Quartic B-splines"> Quartic B-splines</a>, <a href="https://publications.waset.org/abstracts/search?q=solitons" title=" solitons"> solitons</a> </p> <a href="https://publications.waset.org/abstracts/7664/collocation-method-using-quartic-b-splines-for-solving-the-modified-rlw-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/7664.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">304</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">18953</span> Optimal Control of Volterra Integro-Differential Systems Based on Legendre Wavelets and Collocation Method</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Khosrow%20Maleknejad">Khosrow Maleknejad</a>, <a href="https://publications.waset.org/abstracts/search?q=Asyieh%20Ebrahimzadeh"> Asyieh Ebrahimzadeh</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, the numerical solution of optimal control problem (OCP) for systems governed by Volterra integro-differential (VID) equation is considered. The method is developed by means of the Legendre wavelet approximation and collocation method. The properties of Legendre wavelet accompany with Gaussian integration method are utilized to reduce the problem to the solution of nonlinear programming one. Some numerical examples are given to confirm the accuracy and ease of implementation of the method. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=collocation%20method" title="collocation method">collocation method</a>, <a href="https://publications.waset.org/abstracts/search?q=Legendre%20wavelet" title=" Legendre wavelet"> Legendre wavelet</a>, <a href="https://publications.waset.org/abstracts/search?q=optimal%20control" title=" optimal control"> optimal control</a>, <a href="https://publications.waset.org/abstracts/search?q=Volterra%20integro-differential%20equation" title=" Volterra integro-differential equation"> Volterra integro-differential equation</a> </p> <a href="https://publications.waset.org/abstracts/5005/optimal-control-of-volterra-integro-differential-systems-based-on-legendre-wavelets-and-collocation-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/5005.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">388</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">18952</span> Collocation Assessment between GEO and GSO Satellites</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=A.%20E.%20Emam">A. E. Emam</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20Abd%20Elghany"> M. Abd Elghany</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The change in orbit evolution between collocated satellites (X, Y) inside +/-0.09 ° E/W and +/- 0.07 ° N/S cluster, after one of these satellites is placed in an inclined orbit (satellite X) and the effect of this change in the collocation safety inside the cluster window has been studied and evaluated. Several collocation scenarios had been studied in order to adjust the location of both satellites inside their cluster to maximize the separation between them and safe the mission. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=satellite" title="satellite">satellite</a>, <a href="https://publications.waset.org/abstracts/search?q=GEO" title=" GEO"> GEO</a>, <a href="https://publications.waset.org/abstracts/search?q=collocation" title=" collocation"> collocation</a>, <a href="https://publications.waset.org/abstracts/search?q=risk%20assessment" title=" risk assessment"> risk assessment</a> </p> <a href="https://publications.waset.org/abstracts/37245/collocation-assessment-between-geo-and-gso-satellites" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/37245.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">396</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">18951</span> Collocation Method for Coupled System of Boundary Value Problems with Cubic B-Splines </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=K.%20N.%20S.%20Kasi%20Viswanadham">K. N. S. Kasi Viswanadham </a> </p> <p class="card-text"><strong>Abstract:</strong></p> Coupled system of second order linear and nonlinear boundary value problems occur in various fields of Science and Engineering. In the formulation of the problem, any one of 81 possible types of boundary conditions may occur. These 81 possible boundary conditions are written as a combination of four boundary conditions. To solve a coupled system of boundary value problem with these converted boundary conditions, a collocation method with cubic B-splines as basis functions has been developed. In the collocation method, the mesh points of the space variable domain have been selected as the collocation points. The basis functions have been redefined into a new set of basis functions which in number match with the number of mesh points in the space variable domain. The solution of a non-linear boundary value problem has been obtained as the limit of a sequence of solutions of linear boundary value problems generated by quasilinearization technique. Several linear and nonlinear boundary value problems are presented to test the efficiency of the proposed method and found that numerical results obtained by the present method are in good agreement with the exact solutions available in the literature. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=collocation%20method" title="collocation method">collocation method</a>, <a href="https://publications.waset.org/abstracts/search?q=coupled%20system" title=" coupled system"> coupled system</a>, <a href="https://publications.waset.org/abstracts/search?q=cubic%20b-splines" title=" cubic b-splines"> cubic b-splines</a>, <a href="https://publications.waset.org/abstracts/search?q=mesh%20points" title=" mesh points"> mesh points</a> </p> <a href="https://publications.waset.org/abstracts/54713/collocation-method-for-coupled-system-of-boundary-value-problems-with-cubic-b-splines" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/54713.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">209</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">18950</span> Convergence Analysis of Cubic B-Spline Collocation Method for Time Dependent Parabolic Advection-Diffusion Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Bharti%20Gupta">Bharti Gupta</a>, <a href="https://publications.waset.org/abstracts/search?q=V.%20K.%20Kukreja"> V. K. Kukreja</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A comprehensive numerical study is presented for the solution of time-dependent advection diffusion problems by using cubic B-spline collocation method. The linear combination of cubic B-spline basis, taken as approximating function, is evaluated using the zeros of shifted Chebyshev polynomials as collocation points in each element to obtain the best approximation. A comparison, on the basis of efficiency and accuracy, with the previous techniques is made which confirms the superiority of the proposed method. An asymptotic convergence analysis of technique is also discussed, and the method is found to be of order two. The theoretical analysis is supported with suitable examples to show second order convergence of technique. Different numerical examples are simulated using MATLAB in which the 3-D graphical presentation has taken at different time steps as well as different domain of interest. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=cubic%20B-spline%20basis" title="cubic B-spline basis">cubic B-spline basis</a>, <a href="https://publications.waset.org/abstracts/search?q=spectral%20norms" title=" spectral norms"> spectral norms</a>, <a href="https://publications.waset.org/abstracts/search?q=shifted%20Chebyshev%20polynomials" title=" shifted Chebyshev polynomials"> shifted Chebyshev polynomials</a>, <a href="https://publications.waset.org/abstracts/search?q=collocation%20points" title=" collocation points"> collocation points</a>, <a href="https://publications.waset.org/abstracts/search?q=error%20estimates" title=" error estimates"> error estimates</a> </p> <a href="https://publications.waset.org/abstracts/73363/convergence-analysis-of-cubic-b-spline-collocation-method-for-time-dependent-parabolic-advection-diffusion-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/73363.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">18949</span> An Efficient Collocation Method for Solving the Variable-Order Time-Fractional Partial Differential Equations Arising from the Physical Phenomenon</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Haniye%20Dehestani">Haniye Dehestani</a>, <a href="https://publications.waset.org/abstracts/search?q=Yadollah%20Ordokhani"> Yadollah Ordokhani</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this work, we present an efficient approach for solving variable-order time-fractional partial differential equations, which are based on Legendre and Laguerre polynomials. First, we introduced the pseudo-operational matrices of integer and variable fractional order of integration by use of some properties of Riemann-Liouville fractional integral. Then, applied together with collocation method and Legendre-Laguerre functions for solving variable-order time-fractional partial differential equations. Also, an estimation of the error is presented. At last, we investigate numerical examples which arise in physics to demonstrate the accuracy of the present method. In comparison results obtained by the present method with the exact solution and the other methods reveals that the method is very effective. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=collocation%20method" title="collocation method">collocation method</a>, <a href="https://publications.waset.org/abstracts/search?q=fractional%20partial%20differential%20equations" title=" fractional partial differential equations"> fractional partial differential equations</a>, <a href="https://publications.waset.org/abstracts/search?q=legendre-laguerre%20functions" title=" legendre-laguerre functions"> legendre-laguerre functions</a>, <a href="https://publications.waset.org/abstracts/search?q=pseudo-operational%20matrix%20of%20integration" title=" pseudo-operational matrix of integration"> pseudo-operational matrix of integration</a> </p> <a href="https://publications.waset.org/abstracts/97195/an-efficient-collocation-method-for-solving-the-variable-order-time-fractional-partial-differential-equations-arising-from-the-physical-phenomenon" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/97195.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">166</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">18948</span> Constant Order Predictor Corrector Method for the Solution of Modeled Problems of First Order IVPs of ODEs</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=A.%20A.%20James">A. A. James</a>, <a href="https://publications.waset.org/abstracts/search?q=A.%20O.%20Adesanya"> A. O. Adesanya</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20R.%20Odekunle"> M. R. Odekunle</a>, <a href="https://publications.waset.org/abstracts/search?q=D.%20G.%20Yakubu"> D. G. Yakubu</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper examines the development of one step, five hybrid point method for the solution of first order initial value problems. We adopted the method of collocation and interpolation of power series approximate solution to generate a continuous linear multistep method. The continuous linear multistep method was evaluated at selected grid points to give the discrete linear multistep method. The method was implemented using a constant order predictor of order seven over an overlapping interval. The basic properties of the derived corrector was investigated and found to be zero stable, consistent and convergent. The region of absolute stability was also investigated. The method was tested on some numerical experiments and found to compete favorably with the existing methods. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=interpolation" title="interpolation">interpolation</a>, <a href="https://publications.waset.org/abstracts/search?q=approximate%20solution" title=" approximate solution"> approximate solution</a>, <a href="https://publications.waset.org/abstracts/search?q=collocation" title=" collocation"> collocation</a>, <a href="https://publications.waset.org/abstracts/search?q=differential%20system" title=" differential system"> differential system</a>, <a href="https://publications.waset.org/abstracts/search?q=half%20step" title=" half step"> half step</a>, <a href="https://publications.waset.org/abstracts/search?q=converges" title=" converges"> converges</a>, <a href="https://publications.waset.org/abstracts/search?q=block%20method" title=" block method"> block method</a>, <a href="https://publications.waset.org/abstracts/search?q=efficiency" title=" efficiency"> efficiency</a> </p> <a href="https://publications.waset.org/abstracts/1645/constant-order-predictor-corrector-method-for-the-solution-of-modeled-problems-of-first-order-ivps-of-odes" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/1645.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">337</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">18947</span> Starting Order Eight Method Accurately for the Solution of First Order Initial Value Problems of Ordinary Differential Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=James%20Adewale">James Adewale</a>, <a href="https://publications.waset.org/abstracts/search?q=Joshua%20Sunday"> Joshua Sunday</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we developed a linear multistep method, which is implemented in predictor corrector-method. The corrector is developed by method of collocation and interpretation of power series approximate solutions at some selected grid points, to give a continuous linear multistep method, which is evaluated at some selected grid points to give a discrete linear multistep method. The predictors were also developed by method of collocation and interpolation of power series approximate solution, to give a continuous linear multistep method. The continuous linear multistep method is then solved for the independent solution to give a continuous block formula, which is evaluated at some selected grid point to give discrete block method. Basic properties of the corrector were investigated and found to be zero stable, consistent and convergent. The efficiency of the method was tested on some linear, non-learn, oscillatory and stiff problems of first order, initial value problems of ordinary differential equations. The results were found to be better in terms of computer time and error bound when compared with the existing methods. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=predictor" title="predictor">predictor</a>, <a href="https://publications.waset.org/abstracts/search?q=corrector" title=" corrector"> corrector</a>, <a href="https://publications.waset.org/abstracts/search?q=collocation" title=" collocation"> collocation</a>, <a href="https://publications.waset.org/abstracts/search?q=interpolation" title=" interpolation"> interpolation</a>, <a href="https://publications.waset.org/abstracts/search?q=approximate%20solution" title=" approximate solution"> approximate solution</a>, <a href="https://publications.waset.org/abstracts/search?q=independent%20solution" title=" independent solution"> independent solution</a>, <a href="https://publications.waset.org/abstracts/search?q=zero%20stable" title=" zero stable"> zero stable</a>, <a href="https://publications.waset.org/abstracts/search?q=consistent" title=" consistent"> consistent</a>, <a href="https://publications.waset.org/abstracts/search?q=convergent" title=" convergent"> convergent</a> </p> <a href="https://publications.waset.org/abstracts/17775/starting-order-eight-method-accurately-for-the-solution-of-first-order-initial-value-problems-of-ordinary-differential-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/17775.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">501</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">18946</span> Implicit Off-Grid Block Method for Solving Fourth and Fifth Order Ordinary Differential Equations Directly</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Olusola%20Ezekiel%20Abolarin">Olusola Ezekiel Abolarin</a>, <a href="https://publications.waset.org/abstracts/search?q=Gift%20E.%20Noah"> Gift E. Noah</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This research work considered an innovative procedure to numerically approximate higher-order Initial value problems (IVP) of ordinary differential equations (ODE) using the Legendre polynomial as the basis function. The proposed method is a half-step, self-starting Block integrator employed to approximate fourth and fifth order IVPs without reduction to lower order. The method was developed through a collocation and interpolation approach. The basic properties of the method, such as convergence, consistency and stability, were well investigated. Several test problems were considered, and the results compared favorably with both exact solutions and other existing methods. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=initial%20value%20problem" title="initial value problem">initial value problem</a>, <a href="https://publications.waset.org/abstracts/search?q=ordinary%20differential%20equation" title=" ordinary differential equation"> ordinary differential equation</a>, <a href="https://publications.waset.org/abstracts/search?q=implicit%20off-grid%20block%20method" title=" implicit off-grid block method"> implicit off-grid block method</a>, <a href="https://publications.waset.org/abstracts/search?q=collocation" title=" collocation"> collocation</a>, <a href="https://publications.waset.org/abstracts/search?q=interpolation" title=" interpolation"> interpolation</a> </p> <a href="https://publications.waset.org/abstracts/171485/implicit-off-grid-block-method-for-solving-fourth-and-fifth-order-ordinary-differential-equations-directly" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/171485.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">84</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">18945</span> Numerical Solution of Two-Dimensional Solute Transport System Using Operational Matrices</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Shubham%20Jaiswal">Shubham Jaiswal</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this study, the numerical solution of two-dimensional solute transport system in a homogeneous porous medium of finite-length is obtained. The considered transport system have the terms accounting for advection, dispersion and first-order decay with first-type boundary conditions. Initially, the aquifer is considered solute free and a constant input-concentration is considered at inlet boundary. The solution is describing the solute concentration in rectangular inflow-region of the homogeneous porous media. The numerical solution is derived using a powerful method viz., spectral collocation method. The numerical computation and graphical presentations exhibit that the method is effective and reliable during solution of the physical model with complicated boundary conditions even in the presence of reaction term. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=two-dimensional%20solute%20transport%20system" title="two-dimensional solute transport system">two-dimensional solute transport system</a>, <a href="https://publications.waset.org/abstracts/search?q=spectral%20collocation%20method" title=" spectral collocation method"> spectral collocation method</a>, <a href="https://publications.waset.org/abstracts/search?q=Chebyshev%20polynomials" title=" Chebyshev polynomials"> Chebyshev polynomials</a>, <a href="https://publications.waset.org/abstracts/search?q=Chebyshev%20differentiation%20matrix" title=" Chebyshev differentiation matrix"> Chebyshev differentiation matrix</a> </p> <a href="https://publications.waset.org/abstracts/79522/numerical-solution-of-two-dimensional-solute-transport-system-using-operational-matrices" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/79522.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">232</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">18944</span> Convergence of Sinc Methods Applied to Kuramoto-Sivashinsky Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Kamel%20Al-Khaled">Kamel Al-Khaled</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A comparative study of the Sinc-Galerkin and Sinc-Collocation methods for solving the Kuramoto-Sivashinsky equation is given. Both approaches depend on using Sinc basis functions. Firstly, a numerical scheme using Sinc-Galerkin method is developed to approximate the solution of Kuramoto-Sivashinsky equation. Sinc approximations to both derivatives and indefinite integrals reduces the solution to an explicit system of algebraic equations. The error in the solution is shown to converge to the exact solution at an exponential. The convergence proof of the solution for the discrete system is given using fixed-point iteration. Secondly, a combination of a Crank-Nicolson formula in the time direction, with the Sinc-collocation in the space direction is presented, where the derivatives in the space variable are replaced by the necessary matrices to produce a system of algebraic equations. The methods are tested on two examples. The demonstrated results show that both of the presented methods more or less have the same accuracy. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Sinc-Collocation" title="Sinc-Collocation">Sinc-Collocation</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20PDEs" title=" nonlinear PDEs"> nonlinear PDEs</a>, <a href="https://publications.waset.org/abstracts/search?q=numerical%20methods" title=" numerical methods"> numerical methods</a>, <a href="https://publications.waset.org/abstracts/search?q=fixed-point" title=" fixed-point"> fixed-point</a> </p> <a href="https://publications.waset.org/abstracts/9717/convergence-of-sinc-methods-applied-to-kuramoto-sivashinsky-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/9717.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">471</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">18943</span> Numerical Solution of Porous Media Equation Using Jacobi Operational Matrix</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Shubham%20Jaiswal">Shubham Jaiswal</a> </p> <p class="card-text"><strong>Abstract:</strong></p> During modeling of transport phenomena in porous media, many nonlinear partial differential equations (NPDEs) encountered which greatly described the convection, diffusion and reaction process. To solve such types of nonlinear problems, a reliable and efficient technique is needed. In this article, the numerical solution of NPDEs encountered in porous media is derived. Here Jacobi collocation method is used to solve the considered problems which convert the NPDEs in systems of nonlinear algebraic equations that can be solved using Newton-Raphson method. The numerical results of some illustrative examples are reported to show the efficiency and high accuracy of the proposed approach. The comparison of the numerical results with the existing analytical results already reported in the literature and the error analysis for each example exhibited through graphs and tables confirms the exponential convergence rate of the proposed method. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20porous%20media%20equation" title="nonlinear porous media equation">nonlinear porous media equation</a>, <a href="https://publications.waset.org/abstracts/search?q=shifted%20Jacobi%20polynomials" title=" shifted Jacobi polynomials"> shifted Jacobi polynomials</a>, <a href="https://publications.waset.org/abstracts/search?q=operational%20matrix" title=" operational matrix"> operational matrix</a>, <a href="https://publications.waset.org/abstracts/search?q=spectral%20collocation%20method" title=" spectral collocation method"> spectral collocation method</a> </p> <a href="https://publications.waset.org/abstracts/80603/numerical-solution-of-porous-media-equation-using-jacobi-operational-matrix" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/80603.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">439</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">18942</span> Image Transform Based on Integral Equation-Wavelet Approach</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Yuan%20Yan%20Tang">Yuan Yan Tang</a>, <a href="https://publications.waset.org/abstracts/search?q=Lina%20Yang"> Lina Yang</a>, <a href="https://publications.waset.org/abstracts/search?q=Hong%20Li"> Hong Li</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Harmonic model is a very important approximation for the image transform. The harmanic model converts an image into arbitrary shape; however, this mode cannot be described by any fixed functions in mathematics. In fact, it is represented by partial differential equation (PDE) with boundary conditions. Therefore, to develop an efficient method to solve such a PDE is extremely significant in the image transform. In this paper, a novel Integral Equation-Wavelet based method is presented, which consists of three steps: (1) The partial differential equation is converted into boundary integral equation and representation by an indirect method. (2) The boundary integral equation and representation are changed to plane integral equation and representation by boundary measure formula. (3) The plane integral equation and representation are then solved by a method we call wavelet collocation. Our approach has two main advantages, the shape of an image is arbitrary and the program code is independent of the boundary. The performance of our method is evaluated by numerical experiments. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=harmonic%20model" title="harmonic model">harmonic model</a>, <a href="https://publications.waset.org/abstracts/search?q=partial%20differential%20equation%20%28PDE%29" title=" partial differential equation (PDE)"> partial differential equation (PDE)</a>, <a href="https://publications.waset.org/abstracts/search?q=integral%20equation" title=" integral equation"> integral equation</a>, <a href="https://publications.waset.org/abstracts/search?q=integral%20representation" title=" integral representation"> integral representation</a>, <a href="https://publications.waset.org/abstracts/search?q=boundary%20measure%20formula" title=" boundary measure formula"> boundary measure formula</a>, <a href="https://publications.waset.org/abstracts/search?q=wavelet%20collocation" title=" wavelet collocation"> wavelet collocation</a> </p> <a href="https://publications.waset.org/abstracts/3920/image-transform-based-on-integral-equation-wavelet-approach" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/3920.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">558</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">18941</span> Collocation Errors Made by Saudi Learners of English</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Pakenam%20Shiha">Pakenam Shiha</a>, <a href="https://publications.waset.org/abstracts/search?q=Nadine%20Lacsina"> Nadine Lacsina</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Systematic and in-depth analysis of ESL learners’ lexical errors, in general, and of collocation errors, in particular, are relatively rare. Analysis as such proves crucial in understanding how ESL learners construct and use these fixed expressions. Collocational competence of ESL learners is necessary for achieving a native-like proficiency level, which is one of the objectives of foundation programs. This study aims to examine the collocational competence of 50 Saudi foundation program students and identify the collocation errors that they often make. Furthermore, using a questionnaire, the challenges that students encounter in learning collocations and the ways in which their L1 affects their ability to recognize these expressions are identified. To identify the lexical errors and the collocational competence of the students a collocation test was administered. The 150-item lexical collocation test consists of verb-noun and adjective-noun structures. Results of the study reveal that there is a significant difference between the scores of students in the verb-noun and adjective-noun structures. The majority of errors were recorded in the adjective-noun structures due to the students’ L1 influence on the English collocations and the inability to distinguish between synonyms. Moreover, some challenges that students encountered were problems in translation, non-exposure to certain collocations, and degree of L1-L2 difference. All in all, the findings of this study can be interpreted in relation to the student's proficiency level and L2 instruction. Other findings of the study provide insights into language pedagogy—specifically strategies to help students learn collocations more effectively. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=collocations" title="collocations">collocations</a>, <a href="https://publications.waset.org/abstracts/search?q=ESL" title=" ESL"> ESL</a>, <a href="https://publications.waset.org/abstracts/search?q=applied%20linguistics" title=" applied linguistics"> applied linguistics</a>, <a href="https://publications.waset.org/abstracts/search?q=lexical%20collocations" title=" lexical collocations"> lexical collocations</a> </p> <a href="https://publications.waset.org/abstracts/151574/collocation-errors-made-by-saudi-learners-of-english" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/151574.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">122</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">18940</span> Three-Dimensional Optimal Path Planning of a Flying Robot for Terrain Following/Terrain Avoidance</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Amirreza%20Kosari">Amirreza Kosari</a>, <a href="https://publications.waset.org/abstracts/search?q=Hossein%20Maghsoudi"> Hossein Maghsoudi</a>, <a href="https://publications.waset.org/abstracts/search?q=Malahat%20Givar"> Malahat Givar</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this study, the three-dimensional optimal path planning of a flying robot for Terrain Following / Terrain Avoidance (TF/TA) purposes using Direct Collocation has been investigated. To this purpose, firstly, the appropriate equations of motion representing the flying robot translational movement have been described. The three-dimensional optimal path planning of the flying vehicle in terrain following/terrain avoidance maneuver is formulated as an optimal control problem. The terrain profile, as the main allowable height constraint has been modeled using Fractal Generation Method. The resulting optimal control problem is discretized by applying Direct Collocation numerical technique, and then transformed into a Nonlinear Programming Problem (NLP). The efficacy of the proposed method is demonstrated by extensive simulations, and in particular, it is verified that this approach could produce a solution satisfying almost all performance and environmental constraints encountering a low-level flying maneuver <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=path%20planning" title="path planning">path planning</a>, <a href="https://publications.waset.org/abstracts/search?q=terrain%20following" title=" terrain following"> terrain following</a>, <a href="https://publications.waset.org/abstracts/search?q=optimal%20control" title=" optimal control"> optimal control</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20programming" title=" nonlinear programming"> nonlinear programming</a> </p> <a href="https://publications.waset.org/abstracts/98941/three-dimensional-optimal-path-planning-of-a-flying-robot-for-terrain-followingterrain-avoidance" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/98941.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">188</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">18939</span> A New Approach for Solving Fractional Coupled Pdes </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Prashant%20Pandey">Prashant Pandey</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In the present article, an eﬀective Laguerre collocation method is used to obtain the approximate solution of a system of coupled fractional-order non-linear reaction-advection-diﬀusion equation with prescribed initial and boundary conditions. In the proposed scheme, Laguerre polynomials are used together with an operational matrix and collocation method to obtain approximate solutions of the coupled system, so that our proposed model is converted into a system of algebraic equations which can be solved employing the Newton method. The solution proﬁles of the coupled system are presented graphically for diﬀerent particular cases. The salient feature of the present article is ﬁnding the stability analysis of the proposed method and also the demonstration of the lower variation of solute concentrations with respect to the column length in the fractional-order system compared to the integer-order system. To show the higher eﬃciency, reliability, and accuracy of the proposed scheme, a comparison between the numerical results of Burger’s coupled system and its existing analytical result is reported. There are high compatibility and consistency between the approximate solution and its exact solution to a higher order of accuracy. The exhibition of error analysis for each case through tables and graphs conﬁrms the super-linearly convergence rate of the proposed method. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=fractional%20coupled%20PDE" title="fractional coupled PDE">fractional coupled PDE</a>, <a href="https://publications.waset.org/abstracts/search?q=stability%20and%20convergence%20analysis" title=" stability and convergence analysis"> stability and convergence analysis</a>, <a href="https://publications.waset.org/abstracts/search?q=diffusion%20equation" title=" diffusion equation"> diffusion equation</a>, <a href="https://publications.waset.org/abstracts/search?q=Laguerre%20polynomials" title=" Laguerre polynomials"> Laguerre polynomials</a>, <a href="https://publications.waset.org/abstracts/search?q=spectral%20method" title=" spectral method"> spectral method</a> </p> <a href="https://publications.waset.org/abstracts/125320/a-new-approach-for-solving-fractional-coupled-pdes" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/125320.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">145</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">18938</span> Chebyshev Collocation Method for Solving Heat Transfer Analysis for Squeezing Flow of Nanofluid in Parallel Disks</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mustapha%20Rilwan%20Adewale">Mustapha Rilwan Adewale</a>, <a href="https://publications.waset.org/abstracts/search?q=Salau%20Ayobami%20Muhammed"> Salau Ayobami Muhammed</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This study focuses on the heat transfer analysis of magneto-hydrodynamics (MHD) squeezing flow between parallel disks, considering a viscous incompressible fluid. The upper disk exhibits both upward and downward motion, while the lower disk remains stationary but permeable. By employing similarity transformations, a system of nonlinear ordinary differential equations is derived to describe the flow behavior. To solve this system, a numerical approach, namely the Chebyshev collocation method, is utilized. The study investigates the influence of flow parameters and compares the obtained results with existing literature. The significance of this research lies in understanding the heat transfer characteristics of MHD squeezing flow, which has practical implications in various engineering and industrial applications. By employing the similarity transformations, the complex governing equations are simplified into a system of nonlinear ordinary differential equations, facilitating the analysis of the flow behavior. To obtain numerical solutions for the system, the Chebyshev collocation method is implemented. This approach provides accurate approximations for the nonlinear equations, enabling efficient computations of the heat transfer properties. The obtained results are compared with existing literature, establishing the validity and consistency of the numerical approach. The study's major findings shed light on the influence of flow parameters on the heat transfer characteristics of the squeezing flow. The analysis reveals the impact of parameters such as magnetic field strength, disk motion amplitude, fluid viscosity on the heat transfer rate between the disks, the squeeze number(S), suction/injection parameter(A), Hartman number(M), Prandtl number(Pr), modified Eckert number(Ec), and the dimensionless length(δ). These findings contribute to a comprehensive understanding of the system's behavior and provide insights for optimizing heat transfer processes in similar configurations. In conclusion, this study presents a thorough heat transfer analysis of magneto-hydrodynamics squeezing flow between parallel disks. The numerical solutions obtained through the Chebyshev collocation method demonstrate the feasibility and accuracy of the approach. The investigation of flow parameters highlights their influence on heat transfer, contributing to the existing knowledge in this field. The agreement of the results with previous literature further strengthens the reliability of the findings. These outcomes have practical implications for engineering applications and pave the way for further research in related areas. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=squeezing%20flow" title="squeezing flow">squeezing flow</a>, <a href="https://publications.waset.org/abstracts/search?q=magneto-hydro-dynamics%20%28MHD%29" title=" magneto-hydro-dynamics (MHD)"> magneto-hydro-dynamics (MHD)</a>, <a href="https://publications.waset.org/abstracts/search?q=chebyshev%20collocation%20method%28CCA%29" title=" chebyshev collocation method(CCA)"> chebyshev collocation method(CCA)</a>, <a href="https://publications.waset.org/abstracts/search?q=parallel%20manifolds" title=" parallel manifolds"> parallel manifolds</a>, <a href="https://publications.waset.org/abstracts/search?q=finite%20difference%20method%20%28FDM%29" title=" finite difference method (FDM)"> finite difference method (FDM)</a> </p> <a href="https://publications.waset.org/abstracts/169728/chebyshev-collocation-method-for-solving-heat-transfer-analysis-for-squeezing-flow-of-nanofluid-in-parallel-disks" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/169728.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">18937</span> Efficient Numerical Simulation for LDC</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Badr%20Alkahtani">Badr Alkahtani</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this poster, numerical solutions of two-dimensional and three-dimensional lid driven cavity are presented by solving the steady Navier-Stokes equations at high Reynolds numbers where it becomes difficult. Lid driven cavity is where the a fluid contained in a cube and the upper wall is moving. In two dimensions, we use the streamfunction-vorticity formulation to solve the problem in a square domain. A numerical method is employed to discretize the problem in the x and y directions with a spectral collocation method. The problem is coded in the MATLAB programming environment. Solutions at high Reynolds numbers are obtained up to Re=20000 on a fine grid of 131 * 131. Also in this presentation, the numerical solutions for the three-dimensional lid-driven cavity problem are obtained by solving the velocity-vorticity formulation of the Navier-Stokes equations (which is the first time that this has been simulated with special boundary conditions) for various Reynolds numbers. A spectral collocation method is employed to discretize the y and z directions and a finite difference method is used to discretize the x direction. Numerical solutions are obtained for Reynolds number up to 200. , The work prepared here is to show the efficiency of methods used to simulate the physical problem where accurate simulations of lid driven cavity are obtained at high Reynolds number as mentioned above. The result for the two dimensional problem is far from the previous researcher result. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=lid%20driven%20cavity" title="lid driven cavity">lid driven cavity</a>, <a href="https://publications.waset.org/abstracts/search?q=navier-stokes" title=" navier-stokes"> navier-stokes</a>, <a href="https://publications.waset.org/abstracts/search?q=simulation" title=" simulation"> simulation</a>, <a href="https://publications.waset.org/abstracts/search?q=Reynolds%20number" title=" Reynolds number"> Reynolds number</a> </p> <a href="https://publications.waset.org/abstracts/20652/efficient-numerical-simulation-for-ldc" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/20652.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">715</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">18936</span> Turkish University Level EFL Learners’ Collocational Knowledge at Receptive and Productive Levels</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Nazife%20Duygu%20Bagci">Nazife Duygu Bagci</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Collocations are an important part of vocabulary knowledge, and it is a subject that has recently attracted attention, while still in need of more research. The aim of this study is to answer three research questions related to the collocational knowledge of Turkish university level EFL learners at different proficiency levels of English. The first research question aims to compare the pre-intermediate (PIN) and the advanced (ADV) level learners’ collocational knowledge at receptive and productive levels. The second one is to analyze the performance of the PIN and the ADV students in two main collocation categories; lexical and grammatical. Lastly, the performance of both groups are focused on to find the collocation type (among verb-noun, adjective- noun, adjective-preposition, noun-preposition collocation types) they show the best performance in. Two offline tests were used to answer these questions. The results show that there is a significant difference between the PIN and the ADV groups at both receptive and productive levels. It can be concluded that proficiency is an important criterion in collocational knowledge, and learners do not necessarily know the collocates of the vocabulary items that they know. Although there is no significant difference between the PIN group’s performance in lexical and grammatical collocations, the ADV group showed a better performance in lexical collocations. Lastly, the PIN group at receptive and the ADV group at both receptive and productive levels showed the best performance in verb-noun collocations, which is in line with the previous research focusing on different collocation types. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=collocational%20knowledge" title="collocational knowledge">collocational knowledge</a>, <a href="https://publications.waset.org/abstracts/search?q=EFL" title=" EFL"> EFL</a>, <a href="https://publications.waset.org/abstracts/search?q=language%20proficiency" title=" language proficiency"> language proficiency</a>, <a href="https://publications.waset.org/abstracts/search?q=testing" title=" testing"> testing</a> </p> <a href="https://publications.waset.org/abstracts/36902/turkish-university-level-efl-learners-collocational-knowledge-at-receptive-and-productive-levels" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/36902.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">389</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">18935</span> Numerical Solution of Space Fractional Order Linear/Nonlinear Reaction-Advection Diffusion Equation Using Jacobi Polynomial</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Shubham%20Jaiswal">Shubham Jaiswal</a> </p> <p class="card-text"><strong>Abstract:</strong></p> During modelling of many physical problems and engineering processes, fractional calculus plays an important role. Those are greatly described by fractional differential equations (FDEs). So a reliable and efficient technique to solve such types of FDEs is needed. In this article, a numerical solution of a class of fractional differential equations namely space fractional order reaction-advection dispersion equations subject to initial and boundary conditions is derived. In the proposed approach shifted Jacobi polynomials are used to approximate the solutions together with shifted Jacobi operational matrix of fractional order and spectral collocation method. The main advantage of this approach is that it converts such problems in the systems of algebraic equations which are easier to be solved. The proposed approach is effective to solve the linear as well as non-linear FDEs. To show the reliability, validity and high accuracy of proposed approach, the numerical results of some illustrative examples are reported, which are compared with the existing analytical results already reported in the literature. The error analysis for each case exhibited through graphs and tables confirms the exponential convergence rate of the proposed method. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=space%20fractional%20order%20linear%2Fnonlinear%20reaction-advection%20diffusion%20equation" title="space fractional order linear/nonlinear reaction-advection diffusion equation">space fractional order linear/nonlinear reaction-advection diffusion equation</a>, <a href="https://publications.waset.org/abstracts/search?q=shifted%20Jacobi%20polynomials" title=" shifted Jacobi polynomials"> shifted Jacobi polynomials</a>, <a href="https://publications.waset.org/abstracts/search?q=operational%20matrix" title=" operational matrix"> operational matrix</a>, <a href="https://publications.waset.org/abstracts/search?q=collocation%20method" title=" collocation method"> collocation method</a>, <a href="https://publications.waset.org/abstracts/search?q=Caputo%20derivative" title=" Caputo derivative"> Caputo derivative</a> </p> <a href="https://publications.waset.org/abstracts/79521/numerical-solution-of-space-fractional-order-linearnonlinear-reaction-advection-diffusion-equation-using-jacobi-polynomial" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/79521.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">445</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">18934</span> Formulation of Corrector Methods from 3-Step Hybid Adams Type Methods for the Solution of First Order Ordinary Differential Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Y.%20A.%20Yahaya">Y. A. Yahaya</a>, <a href="https://publications.waset.org/abstracts/search?q=Ahmad%20Tijjani%20Asabe"> Ahmad Tijjani Asabe</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper focuses on the formulation of 3-step hybrid Adams type method for the solution of first order differential equation (ODE). The methods which was derived on both grid and off grid points using multistep collocation schemes and also evaluated at some points to produced Block Adams type method and Adams moulton method respectively. The method with the highest order was selected to serve as the corrector. The convergence was valid and efficient. The numerical experiments were carried out and reveal that hybrid Adams type methods performed better than the conventional Adams moulton method. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=adam-moulton%20type%20%28amt%29" title="adam-moulton type (amt)">adam-moulton type (amt)</a>, <a href="https://publications.waset.org/abstracts/search?q=corrector%20method" title=" corrector method"> corrector method</a>, <a href="https://publications.waset.org/abstracts/search?q=off-grid" title=" off-grid"> off-grid</a>, <a href="https://publications.waset.org/abstracts/search?q=block%20method" title=" block method"> block method</a>, <a href="https://publications.waset.org/abstracts/search?q=convergence%20analysis" title=" convergence analysis"> convergence analysis</a> </p> <a href="https://publications.waset.org/abstracts/31263/formulation-of-corrector-methods-from-3-step-hybid-adams-type-methods-for-the-solution-of-first-order-ordinary-differential-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/31263.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">626</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">18933</span> Block Implicit Adams Type Algorithms for Solution of First Order Differential Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Asabe%20Ahmad%20Tijani">Asabe Ahmad Tijani</a>, <a href="https://publications.waset.org/abstracts/search?q=Y.%20A.%20Yahaya"> Y. A. Yahaya</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The paper considers the derivation of implicit Adams-Moulton type method, with k=4 and 5. We adopted the method of interpolation and collocation of power series approximation to generate the continuous formula which was evaluated at off-grid and some grid points within the step length to generate the proposed block schemes, the schemes were investigated and found to be consistent and zero stable. Finally, the methods were tested with numerical experiments to ascertain their level of accuracy. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Adam-Moulton%20Type%20%28AMT%29" title="Adam-Moulton Type (AMT)">Adam-Moulton Type (AMT)</a>, <a href="https://publications.waset.org/abstracts/search?q=off-grid" title=" off-grid"> off-grid</a>, <a href="https://publications.waset.org/abstracts/search?q=block%20%20method" title=" block method"> block method</a>, <a href="https://publications.waset.org/abstracts/search?q=consistent%20and%20zero%20stable" title=" consistent and zero stable"> consistent and zero stable</a> </p> <a href="https://publications.waset.org/abstracts/24946/block-implicit-adams-type-algorithms-for-solution-of-first-order-differential-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/24946.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">482</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">18932</span> Numerical Treatment of Block Method for the Solution of Ordinary Differential Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=A.%20M.%20Sagir">A. M. Sagir</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Discrete linear multistep block method of uniform order for the solution of first order Initial Value Problems (IVPs) in Ordinary Differential Equations (ODEs) is presented in this paper. The approach of interpolation and collocation approximation are adopted in the derivation of the method which is then applied to first order ordinary differential equations with associated initial conditions. The continuous hybrid formulations enable us to differentiate and evaluate at some grids and off – grid points to obtain four discrete schemes, which were used in block form for parallel or sequential solutions of the problems. Furthermore, a stability analysis and efficiency of the block method are tested on ordinary differential equations, and the results obtained compared favorably with the exact solution. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=block%20method" title="block method">block method</a>, <a href="https://publications.waset.org/abstracts/search?q=first%20order%20ordinary%20differential%20equations" title=" first order ordinary differential equations"> first order ordinary differential equations</a>, <a href="https://publications.waset.org/abstracts/search?q=hybrid" title=" hybrid"> hybrid</a>, <a href="https://publications.waset.org/abstracts/search?q=self-starting" title=" self-starting "> self-starting </a> </p> <a href="https://publications.waset.org/abstracts/3426/numerical-treatment-of-block-method-for-the-solution-of-ordinary-differential-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/3426.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">482</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">18931</span> Finite Element Method for Solving the Generalized RLW Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Abdel-Maksoud%20Abdel-Kader%20Soliman">Abdel-Maksoud Abdel-Kader Soliman</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The General Regularized Long Wave (GRLW) equation is solved numerically by giving a new algorithm based on collocation method using quartic B-splines at the mid-knot points as element shape. Also, we use the Fourth Runge-Kutta method for solving the system of first order ordinary differential equations instead of finite difference method. Our test problems, including the migration and interaction of solitary waves, are used to validate the algorithm which is found to be accurate and efficient. The three invariants of the motion are evaluated to determine the conservation properties of the algorithm. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=generalized%20RLW%20equation" title="generalized RLW equation">generalized RLW equation</a>, <a href="https://publications.waset.org/abstracts/search?q=solitons" title=" solitons"> solitons</a>, <a href="https://publications.waset.org/abstracts/search?q=quartic%20b-spline" title=" quartic b-spline"> quartic b-spline</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20partial%20differential%20equations" title=" nonlinear partial differential equations"> nonlinear partial differential equations</a>, <a href="https://publications.waset.org/abstracts/search?q=difference%20equations" title=" difference equations"> difference equations</a> </p> <a href="https://publications.waset.org/abstracts/9023/finite-element-method-for-solving-the-generalized-rlw-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/9023.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">489</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">18930</span> On the Solution of Boundary Value Problems Blended with Hybrid Block Methods</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Kizito%20Ugochukwu%20Nwajeri">Kizito Ugochukwu Nwajeri</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper explores the application of hybrid block methods for solving boundary value problems (BVPs), which are prevalent in various fields such as science, engineering, and applied mathematics. Traditionally, numerical approaches such as finite difference and shooting methods, often encounter challenges related to stability and convergence, particularly in the context of complex and nonlinear BVPs. To address these challenges, we propose a hybrid block method that integrates features from both single-step and multi-step techniques. This method allows for the simultaneous computation of multiple solution points while maintaining high accuracy. Specifically, we employ a combination of polynomial interpolation and collocation strategies to derive a system of equations that captures the behavior of the solution across the entire domain. By directly incorporating boundary conditions into the formulation, we enhance the stability and convergence properties of the numerical solution. Furthermore, we introduce an adaptive step-size mechanism to optimize performance based on the local behavior of the solution. This adjustment allows the method to respond effectively to variations in solution behavior, improving both accuracy and computational efficiency. Numerical tests on a variety of boundary value problems demonstrate the effectiveness of the hybrid block methods. These tests showcase significant improvements in accuracy and computational efficiency compared to conventional methods, indicating that our approach is robust and versatile. The results suggest that this hybrid block method is suitable for a wide range of applications in real-world problems, offering a promising alternative to existing numerical techniques. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=hybrid%20block%20methods" title="hybrid block methods">hybrid block methods</a>, <a href="https://publications.waset.org/abstracts/search?q=boundary%20value%20problem" title=" boundary value problem"> boundary value problem</a>, <a href="https://publications.waset.org/abstracts/search?q=polynomial%20interpolation" title=" polynomial interpolation"> polynomial interpolation</a>, <a href="https://publications.waset.org/abstracts/search?q=adaptive%20step-size%20control" title=" adaptive step-size control"> adaptive step-size control</a>, <a href="https://publications.waset.org/abstracts/search?q=collocation%20methods" title=" collocation methods"> collocation methods</a> </p> <a href="https://publications.waset.org/abstracts/188910/on-the-solution-of-boundary-value-problems-blended-with-hybrid-block-methods" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/188910.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">31</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">18929</span> Cubic Trigonometric B-Spline Approach to Numerical Solution of Wave Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Shazalina%20Mat%20Zin">Shazalina Mat Zin</a>, <a href="https://publications.waset.org/abstracts/search?q=Ahmad%20Abd.%20Majid"> Ahmad Abd. Majid</a>, <a href="https://publications.waset.org/abstracts/search?q=Ahmad%20Izani%20Md.%20Ismail"> Ahmad Izani Md. Ismail</a>, <a href="https://publications.waset.org/abstracts/search?q=Muhammad%20Abbas"> Muhammad Abbas</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The generalized wave equation models various problems in sciences and engineering. In this paper, a new three-time level implicit approach based on cubic trigonometric B-spline for the approximate solution of wave equation is developed. The usual finite difference approach is used to discretize the time derivative while cubic trigonometric B-spline is applied as an interpolating function in the space dimension. Von Neumann stability analysis is used to analyze the proposed method. Two problems are discussed to exhibit the feasibility and capability of the method. The absolute errors and maximum error are computed to assess the performance of the proposed method. The results were found to be in good agreement with known solutions and with existing schemes in literature. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=collocation%20method" title="collocation method">collocation method</a>, <a href="https://publications.waset.org/abstracts/search?q=cubic%20trigonometric%20B-spline" title=" cubic trigonometric B-spline"> cubic trigonometric B-spline</a>, <a href="https://publications.waset.org/abstracts/search?q=finite%20difference" title=" finite difference"> finite difference</a>, <a href="https://publications.waset.org/abstracts/search?q=wave%20equation" title=" wave equation"> wave equation</a> </p> <a href="https://publications.waset.org/abstracts/10136/cubic-trigonometric-b-spline-approach-to-numerical-solution-of-wave-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/10136.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">541</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">18928</span> Comparison of the Boundary Element Method and the Method of Fundamental Solutions for Analysis of Potential and Elasticity</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=S.%20Zenhari">S. Zenhari</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20R.%20Hematiyan"> M. R. Hematiyan</a>, <a href="https://publications.waset.org/abstracts/search?q=A.%20Khosravifard"> A. Khosravifard</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20R.%20Feizi"> M. R. Feizi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The boundary element method (BEM) and the method of fundamental solutions (MFS) are well-known fundamental solution-based methods for solving a variety of problems. Both methods are boundary-type techniques and can provide accurate results. In comparison to the finite element method (FEM), which is a domain-type method, the BEM and the MFS need less manual effort to solve a problem. The aim of this study is to compare the accuracy and reliability of the BEM and the MFS. This comparison is made for 2D potential and elasticity problems with different boundary and loading conditions. In the comparisons, both convex and concave domains are considered. Both linear and quadratic elements are employed for boundary element analysis of the examples. The discretization of the problem domain in the BEM, i.e., converting the boundary of the problem into boundary elements, is relatively simple; however, in the MFS, obtaining appropriate locations of collocation and source points needs more attention to obtain reliable solutions. The results obtained from the presented examples show that both methods lead to accurate solutions for convex domains, whereas the BEM is more suitable than the MFS for concave domains. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=boundary%20element%20method" title="boundary element method">boundary element method</a>, <a href="https://publications.waset.org/abstracts/search?q=method%20of%20fundamental%20solutions" title=" method of fundamental solutions"> method of fundamental solutions</a>, <a href="https://publications.waset.org/abstracts/search?q=elasticity" title=" elasticity"> elasticity</a>, <a href="https://publications.waset.org/abstracts/search?q=potential%20problem" title=" potential problem"> potential problem</a>, <a href="https://publications.waset.org/abstracts/search?q=convex%20domain" title=" convex domain"> convex domain</a>, <a href="https://publications.waset.org/abstracts/search?q=concave%20domain" title=" concave domain"> concave domain</a> </p> <a href="https://publications.waset.org/abstracts/163380/comparison-of-the-boundary-element-method-and-the-method-of-fundamental-solutions-for-analysis-of-potential-and-elasticity" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/163380.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">90</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">18927</span> Analysing Social Media Coverage of Political Speeches in Relation to Discourse and Context</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Yaser%20Mohammed%20Altameemi">Yaser Mohammed Altameemi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This research looks at the representation of the social media for the Saudi Government decrees regarding the developmental projects of the Saudi 2030 vision. The paper analyses a television interview with the Crown Prince Mohammed Bin Salman who talks about the progress of the Saudi vision of 2030, and how the government had acted as response to the COVID-19 pandemic. The interview was on 28/4/2021. The paper analyses the tweets on Twitter that cover the interview for the purpose of investigating the development of concepts and meanings regarding the Saudi peoples’ orientations towards the Saudi projects. The data include all related tweets from the day of the interview and the following seven days after the interview. The finding of the collocation analysis suggests that nationalism notion is explicitly expressed by users in Twitter. The main finding of this paper suggests the importance of further analyses for the concordance lines. However, the collocation network suggests that there is a clear highlight for nationalism. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=social%20media" title="social media">social media</a>, <a href="https://publications.waset.org/abstracts/search?q=twitter" title=" twitter"> twitter</a>, <a href="https://publications.waset.org/abstracts/search?q=political%20interview" title=" political interview"> political interview</a>, <a href="https://publications.waset.org/abstracts/search?q=prince%20Mohammed%20Bin%20Salman" title=" prince Mohammed Bin Salman"> prince Mohammed Bin Salman</a>, <a href="https://publications.waset.org/abstracts/search?q=Saudi%20vision%202030" title=" Saudi vision 2030"> Saudi vision 2030</a> </p> <a href="https://publications.waset.org/abstracts/146201/analysing-social-media-coverage-of-political-speeches-in-relation-to-discourse-and-context" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/146201.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">191</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">18926</span> Numerical Solution of Space Fractional Order Solute Transport System</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Shubham%20Jaiswal">Shubham Jaiswal</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In the present article, a drive is taken to compute the solution of spatial fractional order advection-dispersion equation having source/sink term with given initial and boundary conditions. The equation is converted to a system of ordinary differential equations using second-kind shifted Chebyshev polynomials, which have finally been solved using finite difference method. The striking feature of the article is the fast transportation of solute concentration as and when the system approaches fractional order from standard order for specified values of the parameters of the system. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=spatial%20fractional%20order%20advection-dispersion%20equation" title="spatial fractional order advection-dispersion equation">spatial fractional order advection-dispersion equation</a>, <a href="https://publications.waset.org/abstracts/search?q=second-kind%20shifted%20Chebyshev%20polynomial" title=" second-kind shifted Chebyshev polynomial"> second-kind shifted Chebyshev polynomial</a>, <a href="https://publications.waset.org/abstracts/search?q=collocation%20method" title=" collocation method"> collocation method</a>, <a href="https://publications.waset.org/abstracts/search?q=conservative%20system" title=" conservative system"> conservative system</a>, <a href="https://publications.waset.org/abstracts/search?q=non-conservative%20system" title=" non-conservative system"> non-conservative system</a> </p> <a href="https://publications.waset.org/abstracts/80604/numerical-solution-of-space-fractional-order-solute-transport-system" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/80604.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">261</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=collocation%20method&page=2">2</a></li> <li class="page-item"><a class="page-link" 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