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Journal of Applied Mathematics
Volume 2012, Article ID 365904, 14 pages
http://dx.doi.org/10.1155/2012/365904
Research Article

Numerical Solution of Weakly Singular Integrodifferential Equations on Closed Smooth Contour in Lebesgue Spaces

1Department of Mathematics and Statistics, King Faisal University, Saudi Arabia
2Department of Mathematics, Al-Hussein Bin Talal University, P. O. Box 20 Ma'an, Jordan

Received 18 June 2012; Accepted 3 September 2012

Academic Editor: Yongkun Li

Copyright © 2012 Feras M. Al Faqih. 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 present paper deals with the justification of solvability conditions and properties of solutions for weakly singular integro-differential equations by collocation and mechanical quadrature methods. The equations are defined on an arbitrary smooth closed contour of the complex plane. Error estimates and convergence for the investigated methods are established in Lebesgue spaces.