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Mathematical Problems in Engineering
Volume 2006 (2006), Article ID 96184, 12 pages
http://dx.doi.org/10.1155/MPE/2006/96184

Semiorthogonal spline wavelets approximation for Fredholm integro-differential equations

1Department of Applied Mathematics, Amirkabir University of Technology, Tehran 15914, Iran
2Department of Mathematics and Statistics, Mississippi State University, MS 39762, USA

Received 18 February 2005; Revised 11 May 2005; Accepted 20 June 2005

Copyright © 2006 M. Lakestani 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

A method for solving the nonlinear second-order Fredholm integro-differential equations is presented. The approach is based on a compactly supported linear semiorthogonal B-spline wavelets. The operational matrices of derivative for B-spline scaling functions and wavelets are presented and utilized to reduce the solution of Fredholm integro-differential to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.