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
Descripción
Sumario: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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