A semi-discrete scheme for solving nonlinear hyperbolic-type partial integro-differential equations using radial basis functions

Abstract

In this paper, we propose an effective numerical method for solving nonlinear Volterra partial integro-differential equations. These equations include the partial differentiations of an unknown function and the integral term containing the unknown function as the “memory” of system. Radial basis functions and finite difference method as the main techniques play the important role to reduce a nonlinear partial integro-differential equation to a linear system of equations. Some examples are demonstrated to describe the method. Numerical results confirm the validity and efficiency of the presented method.