The Scientific World Journal (Jan 2014)

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
https://doi.org/10.1155/2014/928765
Journal volume & issue
Vol. 2014

Abstract

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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.