The Numerical Solution of Nonlinear Fredholm-hammerstein Integral Equations of the Second Kind Utilizing Chebyshev Wavelets
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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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ISRP Style
M. M. Shamooshaky, P. Assari, H. Adibi, The Numerical Solution of Nonlinear Fredholm-hammerstein Integral Equations of the Second Kind Utilizing Chebyshev Wavelets, Journal of Mathematics and Computer Science, 10 (2014), no. 4, 235-246
AMA Style
Shamooshaky M. M., Assari P., Adibi H., The Numerical Solution of Nonlinear Fredholm-hammerstein Integral Equations of the Second Kind Utilizing Chebyshev Wavelets. J Math Comput SCI-JM. (2014); 10(4):235-246
Chicago/Turabian Style
Shamooshaky, M. M., Assari, P., Adibi, H.. "The Numerical Solution of Nonlinear Fredholm-hammerstein Integral Equations of the Second Kind Utilizing Chebyshev Wavelets." Journal of Mathematics and Computer Science, 10, no. 4 (2014): 235-246
Keywords
- Fredholm-Hammerstein integral equation
- Chebyshev wavelet
- Galerkin method
- Gauss- Chebyshev quadrature rule
- sparse matrix
MSC
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