Couple of the Variational Iteration Method and Legendre Wavelets for Nonlinear Partial Differential Equations

Couple of the Variational Iteration Method and Legendre Wavelets for Nonlinear Partial Differential Equations

This paper develops a modified variational iteration method coupled with the Legendre wavelets, which can be used for the efficient numerical solution of nonlinear partial differential equations (PDEs). The approximate solutions of PDEs are calculated in the form of a series whose components are com...

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Main Authors: Fukang Yin, Junqiang Song, Xiaoqun Cao, Fengshun Lu
Format: Article
Language:English
Published: Hindawi Limited 2013-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2013/157956
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spelling doaj-576fff6ecd124f4187b0e4f2ff49b8382020-11-25T00:30:06ZengHindawi LimitedJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/157956157956Couple of the Variational Iteration Method and Legendre Wavelets for Nonlinear Partial Differential EquationsFukang Yin0Junqiang Song1Xiaoqun Cao2Fengshun Lu3College of Computer, National University of Defense Technology, Changsha 410073, ChinaCollege of Computer, National University of Defense Technology, Changsha 410073, ChinaCollege of Computer, National University of Defense Technology, Changsha 410073, ChinaChina Aerodynamics Research and Development Center, Mianyang, Sichuan 621000, ChinaThis paper develops a modified variational iteration method coupled with the Legendre wavelets, which can be used for the efficient numerical solution of nonlinear partial differential equations (PDEs). The approximate solutions of PDEs are calculated in the form of a series whose components are computed by applying a recursive relation. Block pulse functions are used to calculate the Legendre wavelets coefficient matrices of the nonlinear terms. The main advantage of the new method is that it can avoid solving the nonlinear algebraic system and symbolic computation. Furthermore, the developed vector-matrix form makes it computationally efficient. The results show that the proposed method is very effective and easy to implement.http://dx.doi.org/10.1155/2013/157956
collection DOAJ
language English
format Article
sources DOAJ
author Fukang Yin
Junqiang Song
Xiaoqun Cao
Fengshun Lu
spellingShingle Fukang Yin
Junqiang Song
Xiaoqun Cao
Fengshun Lu
Couple of the Variational Iteration Method and Legendre Wavelets for Nonlinear Partial Differential Equations
Journal of Applied Mathematics
author_facet Fukang Yin
Junqiang Song
Xiaoqun Cao
Fengshun Lu
author_sort Fukang Yin
title Couple of the Variational Iteration Method and Legendre Wavelets for Nonlinear Partial Differential Equations
title_short Couple of the Variational Iteration Method and Legendre Wavelets for Nonlinear Partial Differential Equations
title_full Couple of the Variational Iteration Method and Legendre Wavelets for Nonlinear Partial Differential Equations
title_fullStr Couple of the Variational Iteration Method and Legendre Wavelets for Nonlinear Partial Differential Equations
title_full_unstemmed Couple of the Variational Iteration Method and Legendre Wavelets for Nonlinear Partial Differential Equations
title_sort couple of the variational iteration method and legendre wavelets for nonlinear partial differential equations
publisher Hindawi Limited
series Journal of Applied Mathematics
issn 1110-757X
1687-0042
publishDate 2013-01-01
description This paper develops a modified variational iteration method coupled with the Legendre wavelets, which can be used for the efficient numerical solution of nonlinear partial differential equations (PDEs). The approximate solutions of PDEs are calculated in the form of a series whose components are computed by applying a recursive relation. Block pulse functions are used to calculate the Legendre wavelets coefficient matrices of the nonlinear terms. The main advantage of the new method is that it can avoid solving the nonlinear algebraic system and symbolic computation. Furthermore, the developed vector-matrix form makes it computationally efficient. The results show that the proposed method is very effective and easy to implement.
url http://dx.doi.org/10.1155/2013/157956
work_keys_str_mv AT fukangyin coupleofthevariationaliterationmethodandlegendrewaveletsfornonlinearpartialdifferentialequations
AT junqiangsong coupleofthevariationaliterationmethodandlegendrewaveletsfornonlinearpartialdifferentialequations
AT xiaoquncao coupleofthevariationaliterationmethodandlegendrewaveletsfornonlinearpartialdifferentialequations
AT fengshunlu coupleofthevariationaliterationmethodandlegendrewaveletsfornonlinearpartialdifferentialequations
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