Taylor collocation method for solving two‐dimensional partial Volterra integro‐differential equations

Abstract

In this paper, the numerical solution of a two-dimensional partial Volterra integro-differential equation (2D-PVIDE) is provided by extending the Taylor collocation scheme of one-dimensional Volterra integral equations. The method is based on the use of Taylor polynomials in two-dimensional, while the approximate solution is given by using explicit schemes. The method is proved to be high-order convergent with respect to the maximum norm. Some numerical examples are given to verify the theoretical results.