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Advances in Mathematical Physics
Volume 2014, Article ID 307907, 12 pages
http://dx.doi.org/10.1155/2014/307907
Research Article

Convergence Analysis of Legendre Pseudospectral Scheme for Solving Nonlinear Systems of Volterra Integral Equations

1Young Researchers and Elite Club, Mashhad Branch, Islamic Azad University, Mashhad, Iran
2Institute for Groundwater Studies, Faculty of Natural and Agricultural Sciences, University of the Free State, Bloemfontein 9300, South Africa

Received 27 December 2013; Revised 1 July 2014; Accepted 16 July 2014; Published 12 August 2014

Academic Editor: Hagen Neidhardt

Copyright © 2014 Emran Tohidi et al. 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

We are concerned with the extension of a Legendre spectral method to the numerical solution of nonlinear systems of Volterra integral equations of the second kind. It is proved theoretically that the proposed method converges exponentially provided that the solution is sufficiently smooth. Also, three biological systems which are known as the systems of Lotka-Volterra equations are approximately solved by the presented method. Numerical results confirm the theoretical prediction of the exponential rate of convergence.