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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 929478, 10 pages
http://dx.doi.org/10.1155/2013/929478
Research Article

Numerical Study of Two-Dimensional Volterra Integral Equations by RDTM and Comparison with DTM

1Young Researchers and Elite Club, Ardabil Branch, Islamic Azad University, Ardabil, Iran
2Department of Mathematics and Institute of Mathematical Research, University Putra Malaysia (UPM), 43400 Serdang, Malaysia

Received 17 April 2013; Accepted 10 June 2013

Academic Editor: Santanu Saha Ray

Copyright © 2013 Reza Abazari and Adem Kılıçman. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The two-dimensional Volterra integral equations are solved using more recent semianalytic method, the reduced differential transform method (the so-called RDTM), and compared with the differential transform method (DTM). The concepts of DTM and RDTM are briefly explained, and their application to the two-dimensional Volterra integral equations is studied. The results obtained by DTM and RDTM together are compared with exact solution. As an important result, it is depicted that the RDTM results are more accurate in comparison with those obtained by DTM applied to the same Volterra integral equations. The numerical results reveal that the RDTM is very effective, convenient, and quite accurate compared to the other kind of nonlinear integral equations. It is predicted that the RDTM can be found widely applicable in engineering sciences.