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Abstract and Applied Analysis
Volume 2014, Article ID 975985, 6 pages
http://dx.doi.org/10.1155/2014/975985
Research Article

A New Wavelet Method for Solving a Class of Nonlinear Volterra-Fredholm Integral Equations

School of Engineering, Huazhong Agricultural University, Wuhan, Hubei 430070, China

Received 1 March 2014; Accepted 4 August 2014; Published 28 August 2014

Academic Editor: Changbum Chun

Copyright © 2014 Xiaomin Wang. 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 new approach, Coiflet-type wavelet Galerkin method, is proposed for numerically solving the Volterra-Fredholm integral equations. Based on the Coiflet-type wavelet approximation scheme, arbitrary nonlinear term of the unknown function in an equation can be explicitly expressed. By incorporating such a modified wavelet approximation scheme into the conventional Galerkin method, the nonsingular property of the connection coefficients significantly reduces the computational complexity and achieves high precision in a very simple way. Thus, one can obtain a stable, highly accurate, and efficient numerical method without calculating the connection coefficients in traditional Galerkin method for solving the nonlinear algebraic equations. At last, numerical simulations are performed to show the efficiency of the method proposed.