New computational method for solving some 2-dimensional nonlinear Volterra integro-differential equations

Authors:
Parviz Darania;Jafar Ahmadi Shali;Karim Ivaz
Affiliations:
Department of Mathematics and Computer Science, University of Tabriz, Tabriz, Iran and Center of Industrial Mathematics, University of Tabriz, Tabriz, Iran;Department of Mathematics and Computer Science, University of Tabriz, Tabriz, Iran and Center of Industrial Mathematics, University of Tabriz, Tabriz, Iran and Islamic Azad University, Shabestar B ...;Department of Mathematics and Computer Science, University of Tabriz, Tabriz, Iran and Center of Industrial Mathematics, University of Tabriz, Tabriz, Iran
Venue:
Numerical Algorithms
Year:
2011

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Abstract

The aim of this paper is to present an efficient numerical procedure for solving the two-dimensional nonlinear Volterra integro-differential equations (2-DNVIDE) by two-dimensional differential transform method (2-DDTM). The technique that we used is the differential transform method, which is based on Taylor series expansion. Using the differential transform, 2-DNVIDE can be transformed to algebraic equations, and the resulting algebraic equations are called iterative equations. New theorems for the transformation of integrals and partial differential equations are introduced and proved. The reliability and efficiency of the proposed scheme are demonstrated by some numerical experiments.