Radial basis function generated finite difference method for the solution of sinh-Gordon equation

Abstract

Accuracy of radial basis functions (RBFs) is increased as the shape parameter decreases and produces an ill-conditioned system. To overcome such difficulty, 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 efficiency 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.