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Abstract and Applied Analysis
Volume 2014, Article ID 213296, 11 pages
http://dx.doi.org/10.1155/2014/213296
Research Article

Convergence of Numerical Solution of Generalized Theodorsen’s Nonlinear Integral Equation

1Department of Mathematics, Faculty of Science, King Khalid University, P.O. Box 9004, Abha, Saudi Arabia
2Department of Mathematics, Faculty of Science, Ibb University, P.O. Box 70270, Ibb, Yemen

Received 7 February 2014; Accepted 24 February 2014; Published 2 April 2014

Academic Editor: Samuel Krushkal

Copyright © 2014 Mohamed M. S. Nasser. 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 consider a nonlinear integral equation which can be interpreted as a generalization of Theodorsen’s nonlinear integral equation. This equation arises in computing the conformal mapping between simply connected regions. We present a numerical method for solving the integral equation and prove the uniform convergence of the numerical solution to the exact solution. Numerical results are given for illustration.