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

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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.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, University of Tabriz, Tabriz, Iran

    Parviz Darania, Jafar Ahmadi Shali & Karim Ivaz

  2. Center of Industrial Mathematics, University of Tabriz, Tabriz, Iran

    Parviz Darania, Jafar Ahmadi Shali & Karim Ivaz

  3. Islamic Azad University, Shabestar Branch, Shabestar, Iran

    Jafar Ahmadi Shali

Authors
  1. Parviz Darania
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  2. Jafar Ahmadi Shali
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  3. Karim Ivaz
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Correspondence to Parviz Darania.

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Darania, P., Shali, J.A. & Ivaz, K. New computational method for solving some 2-dimensional nonlinear Volterra integro-differential equations. Numer Algor 57, 125–147 (2011). https://doi.org/10.1007/s11075-010-9419-4

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  • DOI: https://doi.org/10.1007/s11075-010-9419-4

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