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

Fukang Yin; Junqiang Song; Hongze Leng; Fengshun Lu

doi:10.1155/2014/928765

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

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

Authors

Fukang Yin¹, Junqiang Song¹, Hongze Leng¹, Fengshun Lu²

Affiliations

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.

Publication types

Research Support, Non-U.S. Gov't

MeSH terms

Algorithms*
Models, Theoretical*