An improved PC scheme for nonlinear fractional differential equations: Error and stability analysis

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:324

Article

Asl, Mohammad Shahbazi¹  Javidi, Mohammad¹ 

[1] Univ Tabriz, Fac Math Sci, Tabriz, Iran

关键词: Predictor-corrector scheme;    Fractional differential equation;    Caputo derivative;    Volterra integral equation;   

DOI  :  10.1016/j.cam.2017.04.026

来源: Elsevier

【 摘 要 】

A novel computationally effective fractional predictor-corrector (PC) scheme is proposed to solve fractional differential equations involving Caputo derivative. The properties of the Caputo derivative are used to reduce the fractional differential equation into a Volterra integral equation. To design high order numerical solution of FDEs, the Simpson's 3/8 rule is applied to the Volterra type integral equation. The scheme is capable of handling both linear and nonlinear fractional differential equations. A detailed error analysis and stability analysis of the numerical scheme are rigorously established. The proposed scheme is compared with the PC schemes of literature for illustrating the effectiveness of the algorithm. (C) 2017 Published by Elsevier B.V.

【 授权许可】

Free