High Order Numerical Method for System of Fractional Differential Equations

Authors

Luan Xin, 1.College of Information Science & Engineering, Ocean University of China, Qingdao 266100, China; ;
Xin Jia, 1.College of Information Science & Engineering, Ocean University of China, Qingdao 266100, China; ;
Dalei Song, 2.College of Engineering, Ocean University of China, Qingdao 266100, China; ;
Weijia Zhao, 3.College of Mathematics & Statistics, Qingdao University, Qingdao 266071, China;;

Abstract

Abstract: A spectral deferred correction method for classical ordinary differential equations is extended and reconstructed to solve a system of fractional differential equations (FDES) by accelerating the convergence of lower order schemes. Based on the residual function and the error equation deduced from Volterra integral equations equivalent to the fractional differential equations, a new high order numerical method for a system of FDES is constructed according to the idea of spectral deferred correction. The proposed method allows that one can use a relatively few nodes to obtain the high accuracy numerical solutions of FDES without the penalty of a huge computational cost due to the non-locality of Caputo derivative. The numerical experiments verify the high accuracy and efficiency of the method.

Recommended Citation

Xin, Luan; Jia, Xin; Song, Dalei; and Zhao, Weijia (2019) "High Order Numerical Method for System of Fractional Differential Equations," Journal of System Simulation: Vol. 30: Iss. 2, Article 7.
DOI: 10.16182/j.issn1004731x.joss.201802007
Available at: https://dc-china-simulation.researchcommons.org/journal/vol30/iss2/7

First Page

421

DOI Link

https://doi.org/10.16182/j.issn1004731x.joss.201802007

Last Page

426

CLC

O241.8

Recommended Citation

Luan Xin, Xin Jia, Song Dalei, Zhao Weijia. High Order Numerical Method for System of Fractional Differential Equations[J]. Journal of System Simulation, 2018, 30(2): 421-426.

DOI

10.16182/j.issn1004731x.joss.201802007