The numerical solution of the two–dimensional sinh-Gordon equation via three meshless methods

In this paper three numerical techniques are proposed for solving the nonlinear sinh-Gordon equation. Firstly, we obtain a time discrete scheme then we use the radial basis functions (RBFs) collocation based on Kansa׳s approach, RBF-pseudospectral (PS) technique and moving least squares (MLS) methods to approximate the spatial derivatives. The aim of this paper is to show that the meshless methods based on the RBFs using collocation approach and MLS are suitable for the treatment of the nonlinear partial differential equations and also we compare the mentioned methods in terms of condition number of coefficient matrix and absolute value of error. Also, several test problems are given that show the acceptable accuracy and efficiency of the proposed schemes.