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Wavelet methods for solving linear and nonlinear singular boundary value problems

In this thesis, wavelet analysis method is proposed for solving singular boundary value problems. Operational matrix of differentiation is introduced. Furthermore, product operational matrix is also presented. Many different examples are solved using Chebyshev wavelet analysis method to confirm t...

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Main Author: Nasab, Aliasghar Kazemi
Format: Thesis
Language:English
Published: 2014
Subjects:
Boundary value problems
Online Access:http://psasir.upm.edu.my/id/eprint/70501/1/FS%202014%2064%20IR.pdf
http://psasir.upm.edu.my/id/eprint/70501/
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spelling my.upm.eprints.705012019-10-30T01:47:11Z http://psasir.upm.edu.my/id/eprint/70501/ Wavelet methods for solving linear and nonlinear singular boundary value problems Nasab, Aliasghar Kazemi In this thesis, wavelet analysis method is proposed for solving singular boundary value problems. Operational matrix of differentiation is introduced. Furthermore, product operational matrix is also presented. Many different examples are solved using Chebyshev wavelet analysis method to confirm the accuracy and the efficiency of wavelet analysis method. An efficient and accurate method based on hybrid of Chebyshev wavelets and finite difference methods is introduced for solving linear and nonlinear singular ordinary differential equations such as Lane-Emden equations, boundary value problems of fractional order and singular and nonsingular systems of boundary and initial value problems. High-order multi-point boundary value problems are also solved. The useful properties of Chebyshev wavelets and finite difference method make it a computationally efficient method to approximate the solution of nonlinear equations in a semi-infinite interval. The given problem is converted into a system of algebraic equations using collocation points. The main advantage of this method is the ability to represent smooth and especially piecewise smooth functions properly. It is also clarified that increasing the number of subintervals or the degree of the Chebyshev polynomials in a proper way leads to improvement of the accuracy. Moreover, this method is applicable for solving problems on large interval. Several examples will be provided to demonstrate the powerfulness of the proposed method. A comparison is made among this method, some other well-known approaches and exact solution which confirms that the introduced method are more accurate and efficient. For future studies, some problems are proposed at the end of this thesis. 2014-09 Thesis NonPeerReviewed text en http://psasir.upm.edu.my/id/eprint/70501/1/FS%202014%2064%20IR.pdf Nasab, Aliasghar Kazemi (2014) Wavelet methods for solving linear and nonlinear singular boundary value problems. PhD thesis, Universiti Putra Malaysia. Boundary value problems
institution Universiti Putra Malaysia
building UPM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Putra Malaysia
content_source UPM Institutional Repository
url_provider http://psasir.upm.edu.my/
language English
topic Boundary value problems
spellingShingle Boundary value problems
Nasab, Aliasghar Kazemi
Wavelet methods for solving linear and nonlinear singular boundary value problems
description In this thesis, wavelet analysis method is proposed for solving singular boundary value problems. Operational matrix of differentiation is introduced. Furthermore, product operational matrix is also presented. Many different examples are solved using Chebyshev wavelet analysis method to confirm the accuracy and the efficiency of wavelet analysis method. An efficient and accurate method based on hybrid of Chebyshev wavelets and finite difference methods is introduced for solving linear and nonlinear singular ordinary differential equations such as Lane-Emden equations, boundary value problems of fractional order and singular and nonsingular systems of boundary and initial value problems. High-order multi-point boundary value problems are also solved. The useful properties of Chebyshev wavelets and finite difference method make it a computationally efficient method to approximate the solution of nonlinear equations in a semi-infinite interval. The given problem is converted into a system of algebraic equations using collocation points. The main advantage of this method is the ability to represent smooth and especially piecewise smooth functions properly. It is also clarified that increasing the number of subintervals or the degree of the Chebyshev polynomials in a proper way leads to improvement of the accuracy. Moreover, this method is applicable for solving problems on large interval. Several examples will be provided to demonstrate the powerfulness of the proposed method. A comparison is made among this method, some other well-known approaches and exact solution which confirms that the introduced method are more accurate and efficient. For future studies, some problems are proposed at the end of this thesis.
format Thesis
author Nasab, Aliasghar Kazemi
author_facet Nasab, Aliasghar Kazemi
author_sort Nasab, Aliasghar Kazemi
title Wavelet methods for solving linear and nonlinear singular boundary value problems
title_short Wavelet methods for solving linear and nonlinear singular boundary value problems
title_full Wavelet methods for solving linear and nonlinear singular boundary value problems
title_fullStr Wavelet methods for solving linear and nonlinear singular boundary value problems
title_full_unstemmed Wavelet methods for solving linear and nonlinear singular boundary value problems
title_sort wavelet methods for solving linear and nonlinear singular boundary value problems
publishDate 2014
url http://psasir.upm.edu.my/id/eprint/70501/1/FS%202014%2064%20IR.pdf
http://psasir.upm.edu.my/id/eprint/70501/
_version_ 1651869137209655296
score 13.211869

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