A new differential transformation approach for two-dimensional Volterra integral equations

Abstract

The differential transformation method provides an iterative procedure to obtain the spectrum of analytic solutions. In this paper we extend the differential transformation approach for the solution of two-dimensional integral equations. We give some basic properties and a new differential transformation-type method for the solution of linear and nonlinear two-dimensional Volterra integral equations. By extension of the operations, a two-dimensional integral equation in the domain of interest can be transformed into an algebraic equation in the domain K, H. We show that, after transforming the original equation into an algebraic equation, the coefficients W(k, h) for k, h=1, 2, … are determined and then, by substituting the values of W(k, h) in the transformed equation, the closed form solution of the original equation can be obtained. The reliability and efficiency of the proposed scheme are demonstrated by numerical experiments.

Keywords:

• Differential transformation
• Two-dimensional Volterra integral equations
• Numerical treatments

Acknowledgements

This research was supported, in part, by a grant from IPM (No. 83650039).