title: Couple of the variational iteration method and fractional-order Legendre functions method for fractional differential equations.
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.
authors: College of Computer, National University of Defense Technology, Changsha 410073, China.
authors: Fukang
authors: F
authors: Yin
authors: College of Computer, National University of Defense Technology, Changsha 410073, China.
authors: Junqiang
authors: J
authors: Song
authors: College of Computer, National University of Defense Technology, Changsha 410073, China.
authors: Hongze
authors: H
authors: Leng
authors: China Aerodynamics Research and Development Center, Mianyang, Sichuan 621000, China.
authors: Fengshun
authors: F
authors: Lu
mesh_terms: D000465:Algorithms; D008962:Models, Theoretical