Solving a Nonlinear Multi-Order Fractional Differential Equation Using Legendre Pseudo-Spectral Method

Abstract

In this paper, we apply the Legendre spectral-collocation method to obtain approximate solutions of nonlinear multi-order fractional differential equations (M-FDEs). The fractional derivative is described in the Caputo sense. The study is conducted through illustrative example to demonstrate the validity and applicability of the presented method. The results reveal that the proposed method is very effective and simple. Moreover, only a small number of shifted Legendre polynomials are needed to obtain a satisfactory result.

Keywords

Legendre Pseudo-Spectral Method; Multi-Order Fractional Differential Equations; Caputo Derivative

Legendre Pseudo-Spectral Method; Multi-Order Fractional Differential Equations; Caputo Derivative

Cite this paper

Y. Yang, "Solving a Nonlinear Multi-Order Fractional Differential Equation Using Legendre Pseudo-Spectral Method,"*Applied Mathematics*, Vol. 4 No. 1, 2013, pp. 113-118. doi: 10.4236/am.2013.41020.

Y. Yang, "Solving a Nonlinear Multi-Order Fractional Differential Equation Using Legendre Pseudo-Spectral Method,"

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