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.