RADIAL BASIS FUNCTION GENERATED FINITE DIFFERENCE METHOD FOR THE SOLUTION OF SINH-GORDON EQUATION

RADIAL BASIS FUNCTION GENERATED FINITE DIFFERENCE METHOD FOR THE SOLUTION OF SINH-GORDON EQUATION

J. Rashidinia, M. N. Rasoulizadeh

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Abstract

Accuracy of radial basis functions (RBFs) is increased as the shape parameter decreases and produces an ill-conditioned system. To overcome such diculty, the global stable computation with Gaussian radial basis function-QR (RBF-QR) method was introduced for a limited number of nodes. The main aim of this work is to develop the stable RBF-QR-FD method in order to obtain numerical solutions for the (1 + 2)- dimensional nonlinear sinh-Gordon (ShG) equation. The eciency and accuracy of the presented approach are tested by three examples. A comparison between our results and the three methods such as, RBFs collocation based on Kansa's (RBFK) approach, RBF-Pseudo spectral (RBFPS) and moving least squares (MLS) methods are shown. Furthermore, the stability analysis is proven.

Keywords

Radial basis function(RBF), RBF-QR method, RBF-QR-FD method, sinh- Gordon(ShG) equation, Stability analysis.