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Numerical Solution of the Coupled System of Nonlinear Fractional Ordinary Differential Equations

Part of: Miscellaneous topics - Partial differential equations

Published online by Cambridge University Press:  17 January 2017

Xiaojun Zhou  and
Chuanju Xu
Xiaojun Zhou*
Affiliation:
School of Mathematical Sciences, Guizhou Normal University, Guiyang, Guizhou 550001, China
Chuanju Xu*
Affiliation:
School of Mathematical Sciences, Xiamen University, Xiamen, Fujian 361005, China
*
*Corresponding author. Email:xjzhou@gznu.edu.cn (X. J. Zhou), cjxu@xmu.edu.cn (C. J. Xu)
*Corresponding author. Email:xjzhou@gznu.edu.cn (X. J. Zhou), cjxu@xmu.edu.cn (C. J. Xu)
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Abstract

In this paper, we consider the numerical method that is proposed and analyzed in [J. Cao and C. Xu, J. Comput. Phys., 238 (2013), pp. 154–168] for the fractional ordinary differential equations. It is based on the so-called block-by-block approach, which is a common method for the integral equations. We extend the technique to solve the nonlinear system of fractional ordinary differential equations (FODEs) and present a general technique to construct high order schemes for the numerical solution of the nonlinear coupled system of fractional ordinary differential equations (FODEs). By using the present method, we are able to construct a high order schema for nonlinear system of FODEs of the order α, α>0. The stability and convergence of the schema is rigorously established. Under the smoothness assumption f,g ∈ C4[0,T], we prove that the numerical solution converges to the exact solution with order 3+α for 0<α≤1 and order 4 for α>1. Some numerical examples are provided to confirm the theoretical claims.

Keywords

System of fractional ordinary differential equationshigh order schemastability and convergence analysis

MSC classification

Secondary: 35R11: Fractional partial differential equations
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 9 , Issue 3 , June 2017 , pp. 574 - 595
Copyright
Copyright © Global-Science Press 2017 

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