Chebyshev Wavelet Method for Numerical Solution of Fredholm Integral Equations of the First Kind

Chebyshev Wavelet Method for Numerical Solution of Fredholm Integral Equations of the First Kind

A computational method for solving Fredholm integral equations of the first kind is presented. The method utilizes Chebyshev wavelets constructed on the unit interval as basis in Galerkin method and reduces solving the integral equation to solving a system of algebraic equations. The properties of C...

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Main Authors: Hojatollah Adibi, Pouria Assari
Format: Article
Language:English
Published: Hindawi Limited 2010-01-01
Series:Mathematical Problems in Engineering
Online Access:http://dx.doi.org/10.1155/2010/138408
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spelling doaj-539e37b26d21490398f5fad6eb9785da2020-11-24T21:05:15ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472010-01-01201010.1155/2010/138408138408Chebyshev Wavelet Method for Numerical Solution of Fredholm Integral Equations of the First KindHojatollah Adibi0Pouria Assari1Department of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, No. 424, Hafez Avenue, Tehran 15914, IranDepartment of Applied Mathematics, Faculty of Mathematics and Computer Science, Amirkabir University of Technology, No. 424, Hafez Avenue, Tehran 15914, IranA computational method for solving Fredholm integral equations of the first kind is presented. The method utilizes Chebyshev wavelets constructed on the unit interval as basis in Galerkin method and reduces solving the integral equation to solving a system of algebraic equations. The properties of Chebyshev wavelets are used to make the wavelet coefficient matrices sparse which eventually leads to the sparsity of the coefficients matrix of obtained system. Finally, numerical examples are presented to show the validity and efficiency of the technique.http://dx.doi.org/10.1155/2010/138408
collection DOAJ
language English
format Article
sources DOAJ
author Hojatollah Adibi
Pouria Assari
spellingShingle Hojatollah Adibi
Pouria Assari
Chebyshev Wavelet Method for Numerical Solution of Fredholm Integral Equations of the First Kind
Mathematical Problems in Engineering
author_facet Hojatollah Adibi
Pouria Assari
author_sort Hojatollah Adibi
title Chebyshev Wavelet Method for Numerical Solution of Fredholm Integral Equations of the First Kind
title_short Chebyshev Wavelet Method for Numerical Solution of Fredholm Integral Equations of the First Kind
title_full Chebyshev Wavelet Method for Numerical Solution of Fredholm Integral Equations of the First Kind
title_fullStr Chebyshev Wavelet Method for Numerical Solution of Fredholm Integral Equations of the First Kind
title_full_unstemmed Chebyshev Wavelet Method for Numerical Solution of Fredholm Integral Equations of the First Kind
title_sort chebyshev wavelet method for numerical solution of fredholm integral equations of the first kind
publisher Hindawi Limited
series Mathematical Problems in Engineering
issn 1024-123X
1563-5147
publishDate 2010-01-01
description A computational method for solving Fredholm integral equations of the first kind is presented. The method utilizes Chebyshev wavelets constructed on the unit interval as basis in Galerkin method and reduces solving the integral equation to solving a system of algebraic equations. The properties of Chebyshev wavelets are used to make the wavelet coefficient matrices sparse which eventually leads to the sparsity of the coefficients matrix of obtained system. Finally, numerical examples are presented to show the validity and efficiency of the technique.
url http://dx.doi.org/10.1155/2010/138408
work_keys_str_mv AT hojatollahadibi chebyshevwaveletmethodfornumericalsolutionoffredholmintegralequationsofthefirstkind
AT pouriaassari chebyshevwaveletmethodfornumericalsolutionoffredholmintegralequationsofthefirstkind
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