A not-a-knot meshless method with radial basis functions for numerical solutions of Gilson–Pickering equation

Abstract

In this paper, a numerical meshless method for solving the Gilson–Pickering equation is considered. The method is based on thin-plate radial basis function using collocation points. The scheme proposed works in a similar fashion as finite-difference method and a predictor–corrector scheme is proposed to avoid solving the nonlinear system. In addition, we use the super not-a-knot method for improving the accuracy at the boundaries. The results of numerical experiments are compared with the existing results in illustrative examples to confirm the accuracy and efficiency of the presented scheme and the norm of the error functions is obtained to show the convergence of the method.