Taylor's Meshless Petrov-Galerkin Method for the Numerical Solution of Burger's Equation by Radial Basis Functions | Zendy

Maryam Sarboland | Zendy; A. Aminataei | Zendy

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Taylor's Meshless Petrov-Galerkin Method for the Numerical Solution of Burger's Equation by Radial Basis Functions

Author(s) -

Maryam Sarboland,

A. Aminataei

Publication year - 2012

Publication title -

isrn applied mathematics

Language(s) - English

Resource type - Journals

eISSN - 2090-5572

pISSN - 2090-5564

DOI - 10.5402/2012/254086

Subject(s) - petrov–galerkin method , mathematics , radial basis function , discretization , taylor series , partial differential equation , mathematical analysis , galerkin method , series (stratigraphy) , regularized meshless method , exact solutions in general relativity , nonlinear system , finite element method , singular boundary method , computer science , physics , paleontology , quantum mechanics , machine learning , biology , boundary element method , artificial neural network , thermodynamics

During the last two decades, there has been a considerable interest in developing efficient radial basis functions (RBFs) algorithms for solving partial differential equations (PDEs). In this paper, we introduce the Petrov-Galerkin method for the numerical solution of the one-dimensional nonlinear Burger equation. In this method, the trial space is generated by the multiquadric (MQ) RBF and the test space is generated by the compactly supported RBF. In the time discretization of the equation, the Taylor series expansion is used. This method is applied on some test experiments, and the numerical results have been compared with the exact solutions. The 2, ∞, and root-mean-square (RMS) errors in the solutions show the efficiency and the accuracy of the method.

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