Numerical methods based on radial basis function-generated finite difference (RBF-FD) for solution of GKdVB equation

Abstract

The main aim of present work is to develop the two meshless collocation methods based on radial basis function-generated finite difference (RBF-FD) and global RBF(GRBF) methods to solve the non-linear generalized Korteweg-de Vries-Burgers (GKdVB) equation. For this purpose, at first, we use Taylor expansion to approximate the non-linear terms of the GKdVB equation by linear terms and discretize the temporal derivative with a finite difference scheme. Then we discretize the spatial derivatives with RBF-FD and GRBF methods which give us a linear system of equations. By solving the linear system we get numerical solutions for GKdVB equation. The efficiency and accuracy of these methods are shown with five test problems. Furthermore, the comparisons between the obtained results with spline approximation, RBF collocation, finite element (FEM), HBIM and analytical numerical solution (ANS) methods for some test problems are given. The results show that our methods are more accurate than the mentioned ones.