Couple of the Variational Iteration Method and Fractional-Order Legendre Functions Method for Fractional Differential Equations

We present a new numerical method to get the approximate solutions of fractional differential equations. A new operational matrix of integration for fractional-order Legendre functions (FLFs) is first derived. Then a modified variational iteration formula which can avoid “noise terms” is constructed...

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Detalles Bibliográficos
Autores principales: Yin, Fukang, Song, Junqiang, Leng, Hongze, Lu, Fengshun
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Hindawi Publishing Corporation 2014
Materias:
Research Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3913396/
https://www.ncbi.nlm.nih.gov/pubmed/24511303
http://dx.doi.org/10.1155/2014/928765
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author Yin, Fukang
Song, Junqiang
Leng, Hongze
Lu, Fengshun
author_facet Yin, Fukang
Song, Junqiang
Leng, Hongze
Lu, Fengshun
author_sort Yin, Fukang
collection PubMed
description We present a new numerical method to get the approximate solutions of fractional differential equations. A new operational matrix of integration for fractional-order Legendre functions (FLFs) is first derived. Then a modified variational iteration formula which can avoid “noise terms” is constructed. Finally a numerical method based on variational iteration method (VIM) and FLFs is developed for fractional differential equations (FDEs). Block-pulse functions (BPFs) are used to calculate the FLFs coefficient matrices of the nonlinear terms. Five examples are discussed to demonstrate the validity and applicability of the technique.
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spelling pubmed-39133962014-02-09 Couple of the Variational Iteration Method and Fractional-Order Legendre Functions Method for Fractional Differential Equations Yin, Fukang Song, Junqiang Leng, Hongze Lu, Fengshun ScientificWorldJournal Research Article We present a new numerical method to get the approximate solutions of fractional differential equations. A new operational matrix of integration for fractional-order Legendre functions (FLFs) is first derived. Then a modified variational iteration formula which can avoid “noise terms” is constructed. Finally a numerical method based on variational iteration method (VIM) and FLFs is developed for fractional differential equations (FDEs). Block-pulse functions (BPFs) are used to calculate the FLFs coefficient matrices of the nonlinear terms. Five examples are discussed to demonstrate the validity and applicability of the technique. Hindawi Publishing Corporation 2014-01-05 /pmc/articles/PMC3913396/ /pubmed/24511303 http://dx.doi.org/10.1155/2014/928765 Text en Copyright © 2014 Fukang Yin et al. https://creativecommons.org/licenses/by/3.0/ This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
spellingShingle Research Article
Yin, Fukang
Song, Junqiang
Leng, Hongze
Lu, Fengshun
Couple of the Variational Iteration Method and Fractional-Order Legendre Functions Method for Fractional Differential Equations
title Couple of the Variational Iteration Method and Fractional-Order Legendre Functions Method for Fractional Differential Equations
title_full Couple of the Variational Iteration Method and Fractional-Order Legendre Functions Method for Fractional Differential Equations
title_fullStr Couple of the Variational Iteration Method and Fractional-Order Legendre Functions Method for Fractional Differential Equations
title_full_unstemmed Couple of the Variational Iteration Method and Fractional-Order Legendre Functions Method for Fractional Differential Equations
title_short Couple of the Variational Iteration Method and Fractional-Order Legendre Functions Method for Fractional Differential Equations
title_sort couple of the variational iteration method and fractional-order legendre functions method for fractional differential equations
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3913396/
https://www.ncbi.nlm.nih.gov/pubmed/24511303
http://dx.doi.org/10.1155/2014/928765
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AT lenghongze coupleofthevariationaliterationmethodandfractionalorderlegendrefunctionsmethodforfractionaldifferentialequations
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