Two Efficient Approaches Based On Radial Basis Functions To Nonlinear Time-dependent Partial Differential Equations

Abstract

In this paper, two numerical meshless approaches, based on radial basis functions (RBFs) are applied to solve nonlinear time-dependent partial differential equations. Both of these approaches are based on Kansa meshless method. In these procedures the time is descritized to small time steps, the space is also descritized in each sub-domain. Then by the Kansa collocation method, by using RBFs, the approximate solution, in each step, is obtained. In the first approach, the nonlinear terms are eliminated, by linearization. In the second approach nonlinear equations are solved directly, by Fix point method. Four examples are provided to illustrate the efficiency and the reliability of these approaches. The results are also compared with each other.