Approximate Solutions to Nonlinear Partial Integro-Differential Equations with Applications in Heat Flow

Abstract

In this paper, two different methods based on variational iteration method (VIM) and on differential transform method (DTM) are developed to approximate solutions of some partial integro-differential equations with applications in heat flow. Approximate solutions are obtained for some important physical problems concerned with heat flow in materials with memory. The methods are capable of greatly reducing the size of computational domain. Some numerical examples are presented to show the performances and accuracy of the proposed methods.

Key words and phrases. Variational Iteration Method (VIM), Integro-differential equations, Differential Transform Method (DTM).

2000 Mathematics Subject Classification. 35A15, 65R20, 34A45