A meshless method using radial basis functions for numerical solution of the two-dimensional KdV-Burgers equation

The aim of this article is to obtain the numerical solution of the two-dimensional KdV-Burgers equation. We construct the solution by using a different approach, that is based on using collocation points. The solution is based on using the thin plate splines radial basis function, which builds an approximated solution with discretizing the time and the space to small steps. We use a predictor-corrector scheme to avoid solving the nonlinear system. The results of numerical experiments are compared with analytical solutions to confirm the accuracy and efficiency of the presented scheme.