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  • Küçük Resim
    Öğe
    Application of a numerical method using radial basis functions to nonlinear partial differential equations
    (Selcuk University Research Center of Applied Mathematics, 2011) Uddin, Marjan; Haq, Sirajul
    In this paper, we propose a meshfree method for numerical solution of various classes of partial differential equations (PDEs), such as the Boussinesq system, Drinefel'd-Sokolov-Wilson equations, and Hirota-Satsuma coupled KdV system. The meshfree algorithm is based on scattered data interpolation along with approximating functions known as radial basis functions (RBFs). The meshfree technique does not require space discretization. A set of scattered nodes provided by initial data is used for solution of the problem. Accuracy of the method is estimated in terms of the error norms L?, L_{?}, number of nodes in the domain of influence, time step size, parameter dependent and parameter independent RBFs, the numerical validation for the above mentioned three types of PDEs is given to check performance of the new approach.
  • Küçük Resim
    Öğe
    Solutions of coupled Burger s, fifth-order KdV and Kawahara equations using differential transform method with Padé approximant
    (Selcuk University Research Center of Applied Mathematics, 2010) Haq, Sirajul; Hussain, Arshad; Islam, Siraj-ul
    We use differential transform method (DTM) with Padapproximant for the solution of a class of nonlinear partial differential equations. Efficiency and simple applicability of the method for the solution of complicated nonlinear partial differential equations are the main highlights of this study. Test problems related to coupled Burger's equation and two different types of nonlinear fifth-order Korteweg-de Vries (FKdV) equations are given to show the effectiveness of the technique. Most of the symbolic and numerical computations are performed using Mathematica software.