The Numerical Solution of Nonlinear Fredholm-hammerstein Integral Equations of the Second Kind Utilizing Chebyshev Wavelets

Volume 10, Issue 4, pp 235-246 http://dx.doi.org/10.22436/jmcs.010.04.01

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Authors

M. M. Shamooshaky - Department of Mathematics, Imam Hossein University, P.O. Box 16895-198, Tehran, Iran. P. Assari - Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, No. 424, Hafez Ave., Tehran 15914, Iran. H. Adibi - Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, No. 424, Hafez Ave., Tehran 15914, Iran.

Abstract

This paper describes a numerical scheme based on the Chebyshev wavelets constructed on the unit interval and the Galerkin method for solving nonlinear Fredholm-Hammerstein integral equations of the second kind. Chebyshev wavelets, as very well localized functions, are considerably effective to estimate an unknown function. The integrals included in the method developed in the current paper are approximated by the Gauss-Chebyshev quadrature rule. The proposed scheme reduces Fredholm- Hammerstein integral equations to the solution of nonlinear systems of algebraic equations. The properties of Chebyshev wavelets are used to make the wavelet coefficient matrix sparse which eventually leads to the sparsity of the coefficients matrix of obtained system. Some illustrative examples are presented to show the validity and efficiency of the new technique.

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Keywords

• Fredholm-Hammerstein integral equation
• Chebyshev wavelet
• Galerkin method
• Gauss- Chebyshev quadrature rule
• sparse matrix

MSC

•  65T60
•  65R20
•  45B05

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