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equations</title> <meta name="description" content="Search results for: N-S equations"> <meta name="keywords" content="N-S equations"> <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 navbar-toggler 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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="N-S equations"> <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> 1836</div> </div> </div> </div> <h1 class="mt-3 mb-3 text-center" style="font-size:1.6rem;">Search results for: N-S equations</h1> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">1836</span> Classification of Equations of Motion</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Amritpal%20Singh%20Nafria">Amritpal Singh Nafria</a>, <a href="https://publications.waset.org/abstracts/search?q=Rohit%20Sharma"> Rohit Sharma</a>, <a href="https://publications.waset.org/abstracts/search?q=Md.%20Shami%20Ansari"> Md. Shami Ansari</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Up to now only five different equations of motion can be derived from velocity time graph without needing to know the normal and frictional forces acting at the point of contact. In this paper we obtained all possible requisite conditions to be considering an equation as an equation of motion. After that we classified equations of motion by considering two equations as fundamental kinematical equations of motion and other three as additional kinematical equations of motion. After deriving these five equations of motion, we examine the easiest way of solving a wide variety of useful numerical problems. At the end of the paper, we discussed the importance and educational benefits of classification of equations of motion. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=velocity-time%20graph" title="velocity-time graph">velocity-time graph</a>, <a href="https://publications.waset.org/abstracts/search?q=fundamental%20equations" title=" fundamental equations"> fundamental equations</a>, <a href="https://publications.waset.org/abstracts/search?q=additional%20equations" title=" additional equations"> additional equations</a>, <a href="https://publications.waset.org/abstracts/search?q=requisite%20conditions" title=" requisite conditions"> requisite conditions</a>, <a href="https://publications.waset.org/abstracts/search?q=importance%20and%20educational%20benefits" title=" importance and educational benefits"> importance and educational benefits</a> </p> <a href="https://publications.waset.org/abstracts/15102/classification-of-equations-of-motion" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/15102.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">787</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">1835</span> Weak Solutions Of Stochastic Fractional Differential Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Lev%20Idels">Lev Idels</a>, <a href="https://publications.waset.org/abstracts/search?q=Arcady%20Ponosov"> Arcady Ponosov</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Stochastic fractional differential equations have recently attracted considerable attention, as they have been used to model real-world processes, which are subject to natural memory effects and measurement uncertainties. Compared to conventional hereditary differential equations, one of the advantages of fractional differential equations is related to more realistic geometric properties of their trajectories that do not intersect in the phase space. In this report, a Peano-like existence theorem for nonlinear stochastic fractional differential equations is proven under very general hypotheses. Several specific classes of equations are checked to satisfy these hypotheses, including delay equations driven by the fractional Brownian motion, stochastic fractional neutral equations and many others. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=delay%20equations" title="delay equations">delay equations</a>, <a href="https://publications.waset.org/abstracts/search?q=operator%20methods" title=" operator methods"> operator methods</a>, <a href="https://publications.waset.org/abstracts/search?q=stochastic%20noise" title=" stochastic noise"> stochastic noise</a>, <a href="https://publications.waset.org/abstracts/search?q=weak%20solutions" title=" weak solutions"> weak solutions</a> </p> <a href="https://publications.waset.org/abstracts/146592/weak-solutions-of-stochastic-fractional-differential-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/146592.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">1834</span> Integrable Heisenberg Ferromagnet Equations with Self-Consistent Potentials</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Gulgassyl%20Nugmanova">Gulgassyl Nugmanova</a>, <a href="https://publications.waset.org/abstracts/search?q=Zhanat%20Zhunussova"> Zhanat Zhunussova</a>, <a href="https://publications.waset.org/abstracts/search?q=Kuralay%20Yesmakhanova"> Kuralay Yesmakhanova</a>, <a href="https://publications.waset.org/abstracts/search?q=Galya%20Mamyrbekova"> Galya Mamyrbekova</a>, <a href="https://publications.waset.org/abstracts/search?q=Ratbay%20Myrzakulov"> Ratbay Myrzakulov </a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we consider some integrable Heisenberg Ferromagnet Equations with self-consistent potentials. We study their Lax representations. In particular we derive their equivalent counterparts in the form of nonlinear Schr\"odinger type equations. We present the integrable reductions of the Heisenberg Ferromagnet Equations with self-consistent potentials. These integrable Heisenberg Ferromagnet Equations with self-consistent potentials describe nonlinear waves in ferromagnets with some additional physical fields. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Heisenberg%20Ferromagnet%20equations" title="Heisenberg Ferromagnet equations">Heisenberg Ferromagnet equations</a>, <a href="https://publications.waset.org/abstracts/search?q=soliton%20equations" title=" soliton equations"> soliton equations</a>, <a href="https://publications.waset.org/abstracts/search?q=equivalence" title=" equivalence"> equivalence</a>, <a href="https://publications.waset.org/abstracts/search?q=Lax%20representation" title=" Lax representation"> Lax representation</a> </p> <a href="https://publications.waset.org/abstracts/27440/integrable-heisenberg-ferromagnet-equations-with-self-consistent-potentials" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/27440.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">457</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">1833</span> Further Results on Modified Variational Iteration Method for the Analytical Solution of Nonlinear Advection Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=A.%20W.%20Gbolagade">A. W. Gbolagade</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20O.%20Olayiwola"> M. O. Olayiwola</a>, <a href="https://publications.waset.org/abstracts/search?q=K.%20O.%20Kareem"> K. O. Kareem</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, further to our result on recent paper on the solution of nonlinear advection equations, we present further results on the nonlinear nonhomogeneous advection equations using a modified variational iteration method. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=lagrange%20multiplier" title="lagrange multiplier">lagrange multiplier</a>, <a href="https://publications.waset.org/abstracts/search?q=non-homogeneous%20equations" title=" non-homogeneous equations"> non-homogeneous equations</a>, <a href="https://publications.waset.org/abstracts/search?q=advection%20equations" title=" advection equations"> advection equations</a>, <a href="https://publications.waset.org/abstracts/search?q=mathematics" title=" mathematics"> mathematics</a> </p> <a href="https://publications.waset.org/abstracts/3945/further-results-on-modified-variational-iteration-method-for-the-analytical-solution-of-nonlinear-advection-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/3945.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">301</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">1832</span> A Unified Fitting Method for the Set of Unified Constitutive Equations for Modelling Microstructure Evolution in Hot Deformation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Chi%20Zhang">Chi Zhang</a>, <a href="https://publications.waset.org/abstracts/search?q=Jun%20Jiang"> Jun Jiang</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Constitutive equations are very important in finite element (FE) modeling, and the accuracy of the material constants in the equations have significant effects on the accuracy of the FE models. A wide range of constitutive equations are available; however, fitting the material constants in the constitutive equations could be complex and time-consuming due to the strong non-linearity and relationship between the constants. This work will focus on the development of a set of unified MATLAB programs for fitting the material constants in the constitutive equations efficiently. Users will only need to supply experimental data in the required format and run the program without modifying functions or precisely guessing the initial values, or finding the parameters in previous works and will be able to fit the material constants efficiently. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=constitutive%20equations" title="constitutive equations">constitutive equations</a>, <a href="https://publications.waset.org/abstracts/search?q=FE%20modelling" title=" FE modelling"> FE modelling</a>, <a href="https://publications.waset.org/abstracts/search?q=MATLAB%20program" title=" MATLAB program"> MATLAB program</a>, <a href="https://publications.waset.org/abstracts/search?q=non-linear%20curve%20fitting" title=" non-linear curve fitting"> non-linear curve fitting</a> </p> <a href="https://publications.waset.org/abstracts/162562/a-unified-fitting-method-for-the-set-of-unified-constitutive-equations-for-modelling-microstructure-evolution-in-hot-deformation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/162562.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">99</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">1831</span> New Insight into Fluid Mechanics of Lorenz Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Yu-Kai%20Ting">Yu-Kai Ting</a>, <a href="https://publications.waset.org/abstracts/search?q=Jia-Ying%20Tu"> Jia-Ying Tu</a>, <a href="https://publications.waset.org/abstracts/search?q=Chung-Chun%20Hsiao"> Chung-Chun Hsiao</a> </p> <p class="card-text"><strong>Abstract:</strong></p> New physical insights into the nonlinear Lorenz equations related to flow resistance is discussed in this work. The chaotic dynamics related to Lorenz equations has been studied in many papers, which is due to the sensitivity of Lorenz equations to initial conditions and parameter uncertainties. However, the physical implication arising from Lorenz equations about convectional motion attracts little attention in the relevant literature. Therefore, as a first step to understand the related fluid mechanics of convectional motion, this paper derives the Lorenz equations again with different forced conditions in the model. Simulation work of the modified Lorenz equations without the viscosity or buoyancy force is discussed. The time-domain simulation results may imply that the states of the Lorenz equations are related to certain flow speed and flow resistance. The flow speed of the underlying fluid system increases as the flow resistance reduces. This observation would be helpful to analyze the coupling effects of different fluid parameters in a convectional model in future work. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Galerkin%20method" title="Galerkin method">Galerkin method</a>, <a href="https://publications.waset.org/abstracts/search?q=Lorenz%20equations" title=" Lorenz equations"> Lorenz equations</a>, <a href="https://publications.waset.org/abstracts/search?q=Navier-Stokes%20equations" title=" Navier-Stokes equations"> Navier-Stokes equations</a>, <a href="https://publications.waset.org/abstracts/search?q=convectional%20motion" title=" convectional motion"> convectional motion</a> </p> <a href="https://publications.waset.org/abstracts/21427/new-insight-into-fluid-mechanics-of-lorenz-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/21427.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">392</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">1830</span> On the Relation between λ-Symmetries and μ-Symmetries of Partial Differential Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Teoman%20Ozer">Teoman Ozer</a>, <a href="https://publications.waset.org/abstracts/search?q=Ozlem%20Orhan"> Ozlem Orhan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This study deals with symmetry group properties and conservation laws of partial differential equations. We give a geometrical interpretation of notion of μ-prolongations of vector fields and of the related concept of μ-symmetry for partial differential equations. We show that these are in providing symmetry reduction of partial differential equations and systems and invariant solutions. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=%CE%BB-symmetry" title="λ-symmetry">λ-symmetry</a>, <a href="https://publications.waset.org/abstracts/search?q=%CE%BC-symmetry" title=" μ-symmetry"> μ-symmetry</a>, <a href="https://publications.waset.org/abstracts/search?q=classification" title=" classification"> classification</a>, <a href="https://publications.waset.org/abstracts/search?q=invariant%20solution" title=" invariant solution"> invariant solution</a> </p> <a href="https://publications.waset.org/abstracts/59662/on-the-relation-between-l-symmetries-and-m-symmetries-of-partial-differential-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/59662.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">319</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">1829</span> Equations of Pulse Propagation in Three-Layer Structure of As2S3 Chalcogenide Plasmonic Nano-Waveguides</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Leila%20Motamed-Jahromi">Leila Motamed-Jahromi</a>, <a href="https://publications.waset.org/abstracts/search?q=Mohsen%20Hatami"> Mohsen Hatami</a>, <a href="https://publications.waset.org/abstracts/search?q=Alireza%20Keshavarz"> Alireza Keshavarz </a> </p> <p class="card-text"><strong>Abstract:</strong></p> This research aims at obtaining the equations of pulse propagation in nonlinear plasmonic waveguides created with As<sub>2</sub>S<sub>3</sub> chalcogenide materials. Via utilizing Helmholtz equation and first-order perturbation theory, two components of electric field are determined within frequency domain. Afterwards, the equations are formulated in time domain. The obtained equations include two coupled differential equations that considers nonlinear dispersion<span dir="RTL">.</span> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20optics" title="nonlinear optics">nonlinear optics</a>, <a href="https://publications.waset.org/abstracts/search?q=plasmonic%20waveguide" title=" plasmonic waveguide"> plasmonic waveguide</a>, <a href="https://publications.waset.org/abstracts/search?q=chalcogenide" title=" chalcogenide"> chalcogenide</a>, <a href="https://publications.waset.org/abstracts/search?q=propagation%20equation" title=" propagation equation"> propagation equation</a> </p> <a href="https://publications.waset.org/abstracts/52758/equations-of-pulse-propagation-in-three-layer-structure-of-as2s3-chalcogenide-plasmonic-nano-waveguides" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/52758.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">417</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">1828</span> Development of Extended Trapezoidal Method for Numerical Solution of Volterra Integro-Differential Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Fuziyah%20Ishak">Fuziyah Ishak</a>, <a href="https://publications.waset.org/abstracts/search?q=Siti%20Norazura%20Ahmad"> Siti Norazura Ahmad</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Volterra integro-differential equations appear in many models for real life phenomena. Since analytical solutions for this type of differential equations are hard and at times impossible to attain, engineers and scientists resort to numerical solutions that can be made as accurately as possible. Conventionally, numerical methods for ordinary differential equations are adapted to solve Volterra integro-differential equations. In this paper, numerical solution for solving Volterra integro-differential equation using extended trapezoidal method is described. Formulae for the integral and differential parts of the equation are presented. Numerical results show that the extended method is suitable for solving first order Volterra integro-differential equations. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=accuracy" title="accuracy">accuracy</a>, <a href="https://publications.waset.org/abstracts/search?q=extended%20trapezoidal%20method" title=" extended trapezoidal method"> extended trapezoidal method</a>, <a href="https://publications.waset.org/abstracts/search?q=numerical%20solution" title=" numerical solution"> numerical solution</a>, <a href="https://publications.waset.org/abstracts/search?q=Volterra%20integro-differential%20equations" title=" Volterra integro-differential equations"> Volterra integro-differential equations</a> </p> <a href="https://publications.waset.org/abstracts/52856/development-of-extended-trapezoidal-method-for-numerical-solution-of-volterra-integro-differential-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/52856.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">425</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">1827</span> Reduced Differential Transform Methods for Solving the Fractional Diffusion Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Yildiray%20Keskin">Yildiray Keskin</a>, <a href="https://publications.waset.org/abstracts/search?q=Omer%20Acan"> Omer Acan</a>, <a href="https://publications.waset.org/abstracts/search?q=Murat%20Akkus"> Murat Akkus</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, the solution of fractional diffusion equations is presented by means of the reduced differential transform method. Fractional partial differential equations have special importance in engineering and sciences. Application of reduced differential transform method to this problem shows the rapid convergence of the sequence constructed by this method to the exact solution. The numerical results show that the approach is easy to implement and accurate when applied to fractional diffusion equations. The method introduces a promising tool for solving many fractional partial differential equations. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=fractional%20diffusion%20equations" title="fractional diffusion equations">fractional diffusion equations</a>, <a href="https://publications.waset.org/abstracts/search?q=Caputo%20fractional%20derivative" title=" Caputo fractional derivative"> Caputo fractional derivative</a>, <a href="https://publications.waset.org/abstracts/search?q=reduced%20differential%20transform%20method" title=" reduced differential transform method"> reduced differential transform method</a>, <a href="https://publications.waset.org/abstracts/search?q=partial" title=" partial"> partial</a> </p> <a href="https://publications.waset.org/abstracts/17526/reduced-differential-transform-methods-for-solving-the-fractional-diffusion-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/17526.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">525</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">1826</span> Serious Digital Video Game for Solving Algebraic Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Liliana%20O.%20Mart%C3%ADnez">Liliana O. Martínez</a>, <a href="https://publications.waset.org/abstracts/search?q=Juan%20E%20Gonz%C3%A1lez"> Juan E González</a>, <a href="https://publications.waset.org/abstracts/search?q=Manuel%20Ram%C3%ADrez-Aranda"> Manuel Ramírez-Aranda</a>, <a href="https://publications.waset.org/abstracts/search?q=Ana%20Cervantes-Herrera"> Ana Cervantes-Herrera</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A serious game category mobile application called Math Dominoes is presented. The main objective of this applications is to strengthen the teaching-learning process of solving algebraic equations and is based on the board game "Double 6" dominoes. Math Dominoes allows the practice of solving first, second-, and third-degree algebraic equations. This application is aimed to students who seek to strengthen their skills in solving algebraic equations in a dynamic, interactive, and fun way, to reduce the risk of failure in subsequent courses that require mastery of this algebraic tool. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=algebra" title="algebra">algebra</a>, <a href="https://publications.waset.org/abstracts/search?q=equations" title=" equations"> equations</a>, <a href="https://publications.waset.org/abstracts/search?q=dominoes" title=" dominoes"> dominoes</a>, <a href="https://publications.waset.org/abstracts/search?q=serious%20games" title=" serious games"> serious games</a> </p> <a href="https://publications.waset.org/abstracts/156059/serious-digital-video-game-for-solving-algebraic-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/156059.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">130</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">1825</span> Global Stability Of Nonlinear Itô Equations And N. V. Azbelev's W-method</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Arcady%20Ponosov.">Arcady Ponosov.</a>, <a href="https://publications.waset.org/abstracts/search?q=Ramazan%20Kadiev"> Ramazan Kadiev</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The work studies the global moment stability of solutions of systems of nonlinear differential Itô equations with delays. A modified regularization method (W-method) for the analysis of various types of stability of such systems, based on the choice of the auxiliaryequations and applications of the theory of positive invertible matrices, is proposed and justified. Development of this method for deterministic functional differential equations is due to N.V. Azbelev and his students. Sufficient conditions for the moment stability of solutions in terms of the coefficients for sufficiently general as well as specific classes of Itô equations are given. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=asymptotic%20stability" title="asymptotic stability">asymptotic stability</a>, <a href="https://publications.waset.org/abstracts/search?q=delay%20equations" title=" delay equations"> delay equations</a>, <a href="https://publications.waset.org/abstracts/search?q=operator%20methods" title=" operator methods"> operator methods</a>, <a href="https://publications.waset.org/abstracts/search?q=stochastic%20noise" title=" stochastic noise"> stochastic noise</a> </p> <a href="https://publications.waset.org/abstracts/143260/global-stability-of-nonlinear-ito-equations-and-n-v-azbelevs-w-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/143260.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">1824</span> Solutions of Fractional Reaction-Diffusion Equations Used to Model the Growth and Spreading of Biological Species</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> Reaction-diffusion equations are commonly used in population biology to model the spread of biological species. In this paper, we propose a fractional reaction-diffusion equation, where the classical second derivative diffusion term is replaced by a fractional derivative of order less than two. Based on the symbolic computation system Mathematica, Adomian decomposition method, developed for fractional differential equations, is directly extended to derive explicit and numerical solutions of space fractional reaction-diffusion equations. The fractional derivative is described in the Caputo sense. Finally, the recent appearance of fractional reaction-diffusion equations as models in some ﬁelds such as cell biology, chemistry, physics, and ﬁnance, makes it necessary to apply the results reported here to some numerical examples. <p class="card-text"><strong>Keywords:</strong> <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=reaction-di%EF%AC%80usion%20equations" title=" reaction-diﬀusion equations"> reaction-diﬀusion equations</a>, <a href="https://publications.waset.org/abstracts/search?q=adomian%20decomposition" title=" adomian decomposition"> adomian decomposition</a>, <a href="https://publications.waset.org/abstracts/search?q=biological%20species" title=" biological species"> biological species</a> </p> <a href="https://publications.waset.org/abstracts/55994/solutions-of-fractional-reaction-diffusion-equations-used-to-model-the-growth-and-spreading-of-biological-species" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/55994.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">375</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">1823</span> Numerical Solution for Integro-Differential Equations by Using Quartic B-Spline Wavelet and Operational Matrices</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=Yaser%20Rostami"> Yaser Rostami</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, semi-orthogonal B-spline scaling functions and wavelets and their dual functions are presented to approximate the solutions of integro-differential equations.The B-spline scaling functions and wavelets, their properties and the operational matrices of derivative for this function are presented to reduce the solution of integro-differential equations to the solution of algebraic equations. Here we compute B-spline scaling functions of degree 4 and their dual, then we will show that by using them we have better approximation results for the solution of integro-differential equations in comparison with less degrees of scaling functions. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=%C4%B1ntegro-differential%20equations" title="ıntegro-differential equations">ıntegro-differential equations</a>, <a href="https://publications.waset.org/abstracts/search?q=quartic%20B-spline%20wavelet" title=" quartic B-spline wavelet"> quartic B-spline wavelet</a>, <a href="https://publications.waset.org/abstracts/search?q=operational%20matrices" title=" operational matrices"> operational matrices</a>, <a href="https://publications.waset.org/abstracts/search?q=dual%20functions" title=" dual functions"> dual functions</a> </p> <a href="https://publications.waset.org/abstracts/5002/numerical-solution-for-integro-differential-equations-by-using-quartic-b-spline-wavelet-and-operational-matrices" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/5002.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">456</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">1822</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">1821</span> Generalization of Tau Approximant and Error Estimate of Integral Form of Tau Methods for Some Class 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.%20I.%20Ma%E2%80%99ali">A. I. Ma’ali</a>, <a href="https://publications.waset.org/abstracts/search?q=R.%20B.%20Adeniyi"> R. B. Adeniyi</a>, <a href="https://publications.waset.org/abstracts/search?q=A.%20Y.%20Badeggi"> A. Y. Badeggi</a>, <a href="https://publications.waset.org/abstracts/search?q=U.%20Mohammed"> U. Mohammed </a> </p> <p class="card-text"><strong>Abstract:</strong></p> An error estimation of the integrated formulation of the Lanczos tau method for some class of ordinary differential equations was reported. This paper is concern with the generalization of tau approximants and their corresponding error estimates for some class of ordinary differential equations (ODEs) characterized by m + s =3 (i.e for m =1, s=2; m=2, s=1; and m=3, s=0) where m and s are the order of differential equations and number of overdetermination, respectively. The general result obtained were validated with some numerical examples. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=approximant" title="approximant">approximant</a>, <a href="https://publications.waset.org/abstracts/search?q=error%20estimate" title=" error estimate"> error estimate</a>, <a href="https://publications.waset.org/abstracts/search?q=tau%20method" title=" tau method"> tau method</a>, <a href="https://publications.waset.org/abstracts/search?q=overdetermination" title=" overdetermination"> overdetermination</a> </p> <a href="https://publications.waset.org/abstracts/16442/generalization-of-tau-approximant-and-error-estimate-of-integral-form-of-tau-methods-for-some-class-of-ordinary-differential-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/16442.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">1820</span> Investigating the Form of the Generalised Equations of Motion of the N-Bob Pendulum and Computing Their Solution Using MATLAB</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Divij%20Gupta">Divij Gupta</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Pendular systems have a range of both mathematical and engineering applications, ranging from modelling the behaviour of a continuous mass-density rope to utilisation as Tuned Mass Dampers (TMD). Thus, it is of interest to study the differential equations governing the motion of such systems. Here we attempt to generalise these equations of motion for the plane compound pendulum with a finite number of N point masses. A Lagrangian approach is taken, and we attempt to find the generalised form for the Euler-Lagrange equations of motion for the i-th bob of the N -bob pendulum. The co-ordinates are parameterized as angular quantities to reduce the number of degrees of freedom from 2N to N to simplify the form of the equations. We analyse the form of these equations up to N = 4 to determine the general form of the equation. We also develop a MATLAB program to compute a solution to the system for a given input value of N and a given set of initial conditions. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=classical%20mechanics" title="classical mechanics">classical mechanics</a>, <a href="https://publications.waset.org/abstracts/search?q=differential%20equation" title=" differential equation"> differential equation</a>, <a href="https://publications.waset.org/abstracts/search?q=lagrangian%20analysis" title=" lagrangian analysis"> lagrangian analysis</a>, <a href="https://publications.waset.org/abstracts/search?q=pendulum" title=" pendulum"> pendulum</a> </p> <a href="https://publications.waset.org/abstracts/113019/investigating-the-form-of-the-generalised-equations-of-motion-of-the-n-bob-pendulum-and-computing-their-solution-using-matlab" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/113019.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">1819</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">1818</span> A Numerical Method for Diffusion and Cahn-Hilliard Equations on Evolving Spherical Surfaces</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Jyh-Yang%20Wu">Jyh-Yang Wu</a>, <a href="https://publications.waset.org/abstracts/search?q=Sheng-Gwo%20Chen"> Sheng-Gwo Chen</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we present a simple effective numerical geometric method to estimate the divergence of a vector field over a curved surface. The conservation law is an important principle in physics and mathematics. However, many well-known numerical methods for solving diffusion equations do not obey conservation laws. Our presented method in this paper combines the divergence theorem with a generalized finite difference method and obeys the conservation law on discrete closed surfaces. We use the similar method to solve the Cahn-Hilliard equations on evolving spherical surfaces and observe stability results in our numerical simulations. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=conservation%20laws" title="conservation laws">conservation laws</a>, <a href="https://publications.waset.org/abstracts/search?q=diffusion%20equations" title=" diffusion equations"> diffusion equations</a>, <a href="https://publications.waset.org/abstracts/search?q=Cahn-Hilliard%20equations" title=" Cahn-Hilliard equations"> Cahn-Hilliard equations</a>, <a href="https://publications.waset.org/abstracts/search?q=evolving%20surfaces" title=" evolving surfaces"> evolving surfaces</a> </p> <a href="https://publications.waset.org/abstracts/56432/a-numerical-method-for-diffusion-and-cahn-hilliard-equations-on-evolving-spherical-surfaces" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/56432.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">494</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">1817</span> Nonhomogeneous Linear Second Order Differential Equations and Resonance through Geogebra Program</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=F.%20Maass">F. Maass</a>, <a href="https://publications.waset.org/abstracts/search?q=P.%20Martin"> P. Martin</a>, <a href="https://publications.waset.org/abstracts/search?q=J.%20Olivares"> J. Olivares</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The aim of this work is the application of the program GeoGebra in teaching the study of nonhomogeneous linear second order differential equations with constant coefficients. Different kind of functions or forces will be considered in the right hand side of the differential equations, in particular, the emphasis will be placed in the case of trigonometrical functions producing the resonance phenomena. In order to obtain this, the frequencies of the trigonometrical functions will be changed. Once the resonances appear, these have to be correlationated with the roots of the second order algebraic equation determined by the coefficients of the differential equation. In this way, the physics and engineering students will understand resonance effects and its consequences in the simplest way. A large variety of examples will be shown, using different kind of functions for the nonhomogeneous part of the differential equations. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=education" title="education">education</a>, <a href="https://publications.waset.org/abstracts/search?q=geogebra" title=" geogebra"> geogebra</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=resonance" title=" resonance"> resonance</a> </p> <a href="https://publications.waset.org/abstracts/90040/nonhomogeneous-linear-second-order-differential-equations-and-resonance-through-geogebra-program" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/90040.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">245</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">1816</span> Series Solutions to Boundary Value Differential Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Armin%20Ardekani">Armin Ardekani</a>, <a href="https://publications.waset.org/abstracts/search?q=Mohammad%20Akbari"> Mohammad Akbari</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We present a method of generating series solutions to large classes of nonlinear differential equations. The method is well suited to be adapted in mathematical software and unlike the available commercial solvers, we are capable of generating solutions to boundary value ODEs and PDEs. Many of the generated solutions converge to closed form solutions. Our method can also be applied to systems of ODEs or PDEs, providing all the solutions efficiently. As examples, we present results to many difficult differential equations in engineering fields. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=computational%20mathematics" title="computational mathematics">computational mathematics</a>, <a href="https://publications.waset.org/abstracts/search?q=differential%20equations" title=" differential equations"> differential equations</a>, <a href="https://publications.waset.org/abstracts/search?q=engineering" title=" engineering"> engineering</a>, <a href="https://publications.waset.org/abstracts/search?q=series" title=" series"> series</a> </p> <a href="https://publications.waset.org/abstracts/54764/series-solutions-to-boundary-value-differential-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/54764.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">336</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">1815</span> Numerical Iteration Method to Find New Formulas for Nonlinear Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Kholod%20Mohammad%20Abualnaja">Kholod Mohammad Abualnaja</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A new algorithm is presented to find some new iterative methods for solving nonlinear equations F(x)=0 by using the variational iteration method. The efficiency of the considered method is illustrated by example. The results show that the proposed iteration technique, without linearization or small perturbation, is very effective and convenient. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=variational%20iteration%20method" title="variational iteration method">variational iteration method</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20equations" title=" nonlinear equations"> nonlinear equations</a>, <a href="https://publications.waset.org/abstracts/search?q=Lagrange%20multiplier" title=" Lagrange multiplier"> Lagrange multiplier</a>, <a href="https://publications.waset.org/abstracts/search?q=algorithms" title=" algorithms "> algorithms </a> </p> <a href="https://publications.waset.org/abstracts/12184/numerical-iteration-method-to-find-new-formulas-for-nonlinear-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/12184.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">545</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">1814</span> System of Linear Equations, Gaussian Elimination</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Rabia%20Khan">Rabia Khan</a>, <a href="https://publications.waset.org/abstracts/search?q=Nargis%20Munir"> Nargis Munir</a>, <a href="https://publications.waset.org/abstracts/search?q=Suriya%20Gharib"> Suriya Gharib</a>, <a href="https://publications.waset.org/abstracts/search?q=Syeda%20Roshana%20Ali"> Syeda Roshana Ali</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper linear equations are discussed in detail along with elimination method. Gaussian elimination and Gauss Jordan schemes are carried out to solve the linear system of equation. This paper comprises of matrix introduction, and the direct methods for linear equations. The goal of this research was to analyze different elimination techniques of linear equations and measure the performance of Gaussian elimination and Gauss Jordan method, in order to find their relative importance and advantage in the field of symbolic and numeric computation. The purpose of this research is to revise an introductory concept of linear equations, matrix theory and forms of Gaussian elimination through which the performance of Gauss Jordan and Gaussian elimination can be measured. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=direct" title="direct">direct</a>, <a href="https://publications.waset.org/abstracts/search?q=indirect" title=" indirect"> indirect</a>, <a href="https://publications.waset.org/abstracts/search?q=backward%20stage" title=" backward stage"> backward stage</a>, <a href="https://publications.waset.org/abstracts/search?q=forward%20stage" title=" forward stage"> forward stage</a> </p> <a href="https://publications.waset.org/abstracts/33569/system-of-linear-equations-gaussian-elimination" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/33569.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">595</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">1813</span> On Boundary Value Problems of Fractional Differential Equations Involving Stieltjes Derivatives</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Baghdad%20Said">Baghdad Said</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Differential equations of fractional order have proved to be important tools to describe many physical phenomena and have been used in diverse fields such as engineering, mathematics as well as other applied sciences. On the other hand, the theory of differential equations involving the Stieltjes derivative (SD) with respect to a non-decreasing function is a new class of differential equations and has many applications as a unified framework for dynamic equations on time scales and differential equations with impulses at fixed times. The aim of this paper is to investigate the existence, uniqueness, and generalized Ulam-Hyers-Rassias stability (UHRS) of solutions for a boundary value problem of sequential fractional differential equations (SFDE) containing (SD). This study is based on the technique of noncompactness measures (MNCs) combined with Monch-Krasnoselski fixed point theorems (FPT), and the results are proven in an appropriate Banach space under sufficient hypotheses. We also give an illustrative example. In this work, we introduced a class of (SFDE) and the results are obtained under a few hypotheses. Future directions connected to this work could focus on another problem with different types of fractional integrals and derivatives, and the (SD) will be assumed under a more general hypothesis in more general functional spaces. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=SFDE" title="SFDE">SFDE</a>, <a href="https://publications.waset.org/abstracts/search?q=SD" title=" SD"> SD</a>, <a href="https://publications.waset.org/abstracts/search?q=UHRS" title=" UHRS"> UHRS</a>, <a href="https://publications.waset.org/abstracts/search?q=MNCs" title=" MNCs"> MNCs</a>, <a href="https://publications.waset.org/abstracts/search?q=FPT" title=" FPT"> FPT</a> </p> <a href="https://publications.waset.org/abstracts/187408/on-boundary-value-problems-of-fractional-differential-equations-involving-stieltjes-derivatives" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/187408.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">40</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">1812</span> Investigation of the Evolutionary Equations of the Two-Planetary Problem of Three Bodies with Variable Masses</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Zhanar%20Imanova">Zhanar Imanova</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Masses of real celestial bodies change anisotropically and reactive forces appear, and they need to be taken into account in the study of these bodies' dynamics. We studied the two-planet problem of three bodies with variable masses in the presence of reactive forces and obtained the equations of perturbed motion in Newton’s form equations. The motion equations in the orbital coordinate system, unlike the Lagrange equation, are convenient for taking into account the reactive forces. The perturbing force is expanded in terms of osculating elements. The expansion of perturbing functions is a time-consuming analytical calculation and results in very cumber some analytical expressions. In the considered problem, we obtained expansions of perturbing functions by small parameters up to and including the second degree. In the non resonant case, we obtained evolution equations in the Newton equation form. All symbolic calculations were done in Wolfram Mathematica. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=two-planet" title="two-planet">two-planet</a>, <a href="https://publications.waset.org/abstracts/search?q=three-body%20problem" title=" three-body problem"> three-body problem</a>, <a href="https://publications.waset.org/abstracts/search?q=variable%20mass" title=" variable mass"> variable mass</a>, <a href="https://publications.waset.org/abstracts/search?q=evolutionary%20equations" title=" evolutionary equations"> evolutionary equations</a> </p> <a href="https://publications.waset.org/abstracts/184634/investigation-of-the-evolutionary-equations-of-the-two-planetary-problem-of-three-bodies-with-variable-masses" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/184634.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">64</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">1811</span> Refitting Equations for Peak Ground Acceleration in Light of the PF-L Database</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Matev%C5%BE%20Bre%C5%A1ka">Matevž Breška</a>, <a href="https://publications.waset.org/abstracts/search?q=Iztok%20Peru%C5%A1"> Iztok Peruš</a>, <a href="https://publications.waset.org/abstracts/search?q=Vlado%20Stankovski"> Vlado Stankovski</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Systematic overview of existing Ground Motion Prediction Equations (GMPEs) has been published by Douglas. The number of earthquake recordings that have been used for fitting these equations has increased in the past decades. The current PF-L database contains 3550 recordings. Since the GMPEs frequently model the peak ground acceleration (PGA) the goal of the present study was to refit a selection of 44 of the existing equation models for PGA in light of the latest data. The algorithm Levenberg-Marquardt was used for fitting the coefficients of the equations and the results are evaluated both quantitatively by presenting the root mean squared error (RMSE) and qualitatively by drawing graphs of the five best fitted equations. The RMSE was found to be as low as 0.08 for the best equation models. The newly estimated coefficients vary from the values published in the original works. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ground%20Motion%20Prediction%20Equations" title="Ground Motion Prediction Equations">Ground Motion Prediction Equations</a>, <a href="https://publications.waset.org/abstracts/search?q=Levenberg-Marquardt%20algorithm" title=" Levenberg-Marquardt algorithm"> Levenberg-Marquardt algorithm</a>, <a href="https://publications.waset.org/abstracts/search?q=refitting%20PF-L%20database" title=" refitting PF-L database"> refitting PF-L database</a>, <a href="https://publications.waset.org/abstracts/search?q=peak%20ground%20acceleration" title=" peak ground acceleration"> peak ground acceleration</a> </p> <a href="https://publications.waset.org/abstracts/15426/refitting-equations-for-peak-ground-acceleration-in-light-of-the-pf-l-database" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/15426.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">462</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">1810</span> Investigating Smoothness: An In-Depth Study of Extremely Degenerate Elliptic Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Zahid%20Ullah">Zahid Ullah</a>, <a href="https://publications.waset.org/abstracts/search?q=Atlas%20Khan"> Atlas Khan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The presented research is dedicated to an extensive examination of the regularity properties associated with a specific class of equations, namely extremely degenerate elliptic equations. This study holds significance in unraveling the complexities inherent in these equations and understanding the smoothness of their solutions. The focus is on analyzing the regularity of results, aiming to contribute to the broader field of mathematical theory. By delving into the intricacies of extremely degenerate elliptic equations, the research seeks to advance our understanding beyond conventional analyses, addressing challenges posed by degeneracy and pushing the boundaries of classical analytical methods. The motivation for this exploration lies in the practical applicability of mathematical models, particularly in real-world scenarios where physical phenomena exhibit characteristics that challenge traditional mathematical modeling. The research aspires to fill gaps in the current understanding of regularity properties within solutions to extremely degenerate elliptic equations, ultimately contributing to both theoretical foundations and practical applications in diverse scientific fields. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=investigating%20smoothness" title="investigating smoothness">investigating smoothness</a>, <a href="https://publications.waset.org/abstracts/search?q=extremely%20degenerate%20elliptic%20equations" title=" extremely degenerate elliptic equations"> extremely degenerate elliptic equations</a>, <a href="https://publications.waset.org/abstracts/search?q=regularity%20properties" title=" regularity properties"> regularity properties</a>, <a href="https://publications.waset.org/abstracts/search?q=mathematical%20analysis" title=" mathematical analysis"> mathematical analysis</a>, <a href="https://publications.waset.org/abstracts/search?q=complexity%20solutions" title=" complexity solutions"> complexity solutions</a> </p> <a href="https://publications.waset.org/abstracts/181742/investigating-smoothness-an-in-depth-study-of-extremely-degenerate-elliptic-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/181742.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">59</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">1809</span> On the Approximate Solution of Continuous Coefficients for Solving Third Order 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> This paper derived four newly schemes which are combined in order to form an accurate and efficient block method for parallel or sequential solution of third order ordinary differential equations of the form y^'''= f(x,y,y^',y^'' ), y(α)=y_0,〖y〗^' (α)=β,y^('' ) (α)=μ with associated initial or boundary conditions. The implementation strategies of the derived method have shown that the block method is found to be consistent, zero stable and hence convergent. The derived schemes were tested on stiff and non-stiff ordinary differential equations, and the numerical 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=hybrid" title=" hybrid"> hybrid</a>, <a href="https://publications.waset.org/abstracts/search?q=linear%20multistep" title=" linear multistep"> linear multistep</a>, <a href="https://publications.waset.org/abstracts/search?q=self-starting" title=" self-starting"> self-starting</a>, <a href="https://publications.waset.org/abstracts/search?q=third%20order%20ordinary%20differential%20equations" title=" third order ordinary differential equations"> third order ordinary differential equations</a> </p> <a href="https://publications.waset.org/abstracts/3659/on-the-approximate-solution-of-continuous-coefficients-for-solving-third-order-ordinary-differential-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/3659.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">271</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">1808</span> The Finite Element Method for Nonlinear Fredholm Integral Equation of the Second Kind</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Melusi%20Khumalo">Melusi Khumalo</a>, <a href="https://publications.waset.org/abstracts/search?q=Anastacia%20Dlamini"> Anastacia Dlamini</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, we consider a numerical solution for nonlinear Fredholm integral equations of the second kind. We work with uniform mesh and use the Lagrange polynomials together with the Galerkin finite element method, where the weight function is chosen in such a way that it takes the form of the approximate solution but with arbitrary coefficients. We implement the finite element method to the nonlinear Fredholm integral equations of the second kind. We consider the error analysis of the method. Furthermore, we look at a specific example to illustrate the implementation of the finite element method. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=finite%20element%20method" title="finite element method">finite element method</a>, <a href="https://publications.waset.org/abstracts/search?q=Galerkin%20approach" title=" Galerkin approach"> Galerkin approach</a>, <a href="https://publications.waset.org/abstracts/search?q=Fredholm%20integral%20equations" title=" Fredholm integral equations"> Fredholm integral equations</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20integral%20equations" title=" nonlinear integral equations"> nonlinear integral equations</a> </p> <a href="https://publications.waset.org/abstracts/140832/the-finite-element-method-for-nonlinear-fredholm-integral-equation-of-the-second-kind" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/140832.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">376</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">1807</span> Algorithms Utilizing Wavelet to Solve Various Partial Differential Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=K.%20P.%20Mredula">K. P. Mredula</a>, <a href="https://publications.waset.org/abstracts/search?q=D.%20C.%20Vakaskar"> D. C. Vakaskar </a> </p> <p class="card-text"><strong>Abstract:</strong></p> The article traces developments and evolution of various algorithms developed for solving partial differential equations using the significant combination of wavelet with few already explored solution procedures. The approach depicts a study over a decade of traces and remarks on the modifications in implementing multi-resolution of wavelet, finite difference approach, finite element method and finite volume in dealing with a variety of partial differential equations in the areas like plasma physics, astrophysics, shallow water models, modified Burger equations used in optical fibers, biology, fluid dynamics, chemical kinetics etc. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=multi-resolution" title="multi-resolution">multi-resolution</a>, <a href="https://publications.waset.org/abstracts/search?q=Haar%20Wavelet" title=" Haar Wavelet"> Haar Wavelet</a>, <a href="https://publications.waset.org/abstracts/search?q=partial%20differential%20equation" title=" partial differential equation"> partial differential equation</a>, <a href="https://publications.waset.org/abstracts/search?q=numerical%20methods" title=" numerical methods"> numerical methods</a> </p> <a href="https://publications.waset.org/abstracts/59280/algorithms-utilizing-wavelet-to-solve-various-partial-differential-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/59280.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">299</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=N-S%20equations&page=2">2</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=N-S%20equations&page=3">3</a></li> <li class="page-item"><a class="page-link" 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