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

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. Thismethod is applied on some test experiments, and the numerical results have been compared with the exact solutions. The L₂, L₈, and root-meansquare (RMS) errors in the solutions show the efficiency and the accuracy of the method. [ABSTRACT FROM AUTHOR]