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Abstract and Applied Analysis
Volume 2012, Article ID 258067, 10 pages
Research Article

The Combined RKM and ADM for Solving Nonlinear Weakly Singular Volterra Integrodifferential Equations

School of Mathematics and Sciences, Harbin Normal University, Heilongjiang, Harbin, 150025, China

Received 2 July 2012; Accepted 12 November 2012

Academic Editor: Natig M. Atakishiyev

Copyright © 2012 Xueqin Lv and Sixing Shi. 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.


The reproducing kernel method (RKM) and the Adomian decomposition method (ADM) are applied to solve th-order nonlinear weakly singular Volterra integrodifferential equations. The numerical solutions of this class of equations have been a difficult topic to analyze. The aim of this paper is to use Taylor’s approximation and then transform the given th-order nonlinear Volterra integrodifferential equation into an ordinary nonlinear differential equation. Using the RKM and ADM to solve ordinary nonlinear differential equation is an accurate and efficient method. Some examples indicate that this method is an efficient method to solve th-order nonlinear Volterra integro-differential equations.