An Efficient Approach for Solving Nonlinear Troesch’s and Bratu’s Problems by Wavelet Analysis Method

An Efficient Approach for Solving Nonlinear Troesch’s and Bratu’s Problems by Wavelet Analysis Method

We introduce Chebyshev wavelet analysis method to solve the nonlinear Troesch and Bratu problems. Chebyshev wavelets expansions together with operational matrix of derivative are employed to reduce the computation of nonlinear problems to a system of algebraic equations. Several examples are given t...

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Main Authors: A. Kazemi Nasab, Z. Pashazadeh Atabakan, A. Kılıçman
Format: Article
Language:English
Published: Hindawi Limited 2013-01-01
Series:Mathematical Problems in Engineering
Online Access:http://dx.doi.org/10.1155/2013/825817
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spelling doaj-ddc72b8388894d669826f96bbc8723ce2020-11-24T20:59:11ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472013-01-01201310.1155/2013/825817825817An Efficient Approach for Solving Nonlinear Troesch’s and Bratu’s Problems by Wavelet Analysis MethodA. Kazemi Nasab0Z. Pashazadeh Atabakan1A. Kılıçman2Department of Mathematics and Mathematical Research Institute, University Putra Malaysia, 43400 Serdang, Selangor, MalaysiaDepartment of Mathematics and Mathematical Research Institute, University Putra Malaysia, 43400 Serdang, Selangor, MalaysiaDepartment of Mathematics and Mathematical Research Institute, University Putra Malaysia, 43400 Serdang, Selangor, MalaysiaWe introduce Chebyshev wavelet analysis method to solve the nonlinear Troesch and Bratu problems. Chebyshev wavelets expansions together with operational matrix of derivative are employed to reduce the computation of nonlinear problems to a system of algebraic equations. Several examples are given to validate the efficiency and accuracy of the proposed technique. We compare the results with those ones reported in the literature in order to demonstrate that the method converges rapidly and approximates the exact solution very accurately by using only a small number of Chebyshev wavelet basis functions. Convergence analysis is also included.http://dx.doi.org/10.1155/2013/825817
collection DOAJ
language English
format Article
sources DOAJ
author A. Kazemi Nasab
Z. Pashazadeh Atabakan
A. Kılıçman
spellingShingle A. Kazemi Nasab
Z. Pashazadeh Atabakan
A. Kılıçman
An Efficient Approach for Solving Nonlinear Troesch’s and Bratu’s Problems by Wavelet Analysis Method
Mathematical Problems in Engineering
author_facet A. Kazemi Nasab
Z. Pashazadeh Atabakan
A. Kılıçman
author_sort A. Kazemi Nasab
title An Efficient Approach for Solving Nonlinear Troesch’s and Bratu’s Problems by Wavelet Analysis Method
title_short An Efficient Approach for Solving Nonlinear Troesch’s and Bratu’s Problems by Wavelet Analysis Method
title_full An Efficient Approach for Solving Nonlinear Troesch’s and Bratu’s Problems by Wavelet Analysis Method
title_fullStr An Efficient Approach for Solving Nonlinear Troesch’s and Bratu’s Problems by Wavelet Analysis Method
title_full_unstemmed An Efficient Approach for Solving Nonlinear Troesch’s and Bratu’s Problems by Wavelet Analysis Method
title_sort efficient approach for solving nonlinear troesch’s and bratu’s problems by wavelet analysis method
publisher Hindawi Limited
series Mathematical Problems in Engineering
issn 1024-123X
1563-5147
publishDate 2013-01-01
description We introduce Chebyshev wavelet analysis method to solve the nonlinear Troesch and Bratu problems. Chebyshev wavelets expansions together with operational matrix of derivative are employed to reduce the computation of nonlinear problems to a system of algebraic equations. Several examples are given to validate the efficiency and accuracy of the proposed technique. We compare the results with those ones reported in the literature in order to demonstrate that the method converges rapidly and approximates the exact solution very accurately by using only a small number of Chebyshev wavelet basis functions. Convergence analysis is also included.
url http://dx.doi.org/10.1155/2013/825817
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