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ScientificWorldJournal. 2014 Jan 5;2014:928765. doi: 10.1155/2014/928765. eCollection 2014.

Couple of the variational iteration method and fractional-order Legendre functions method for fractional differential equations.

Author information

1
College of Computer, National University of Defense Technology, Changsha 410073, China.
2
China Aerodynamics Research and Development Center, Mianyang, Sichuan 621000, China.

Abstract

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.

PMID:
24511303
PMCID:
PMC3913396
DOI:
10.1155/2014/928765
[Indexed for MEDLINE]
Free PMC Article

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