High order algorithms for numerical solution of fractional differential equations

Advances in Difference Equations

article

Asl, Mohammad Shahbazi¹  Javidi, Mohammad¹  Yan, Yubin² 

[1] Department of Mathematics, University of Tabriz;Department of Mathematics, University of Chester

关键词: Numerical algorithm;    Fractional differential equation;    Caputo fractional derivative;    Stability analysis;    Error estimates;   

DOI  :  10.1186/s13662-021-03273-4

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

In this paper, two novel high order numerical algorithms are proposed for solving fractional differential equations where the fractional derivative is considered in the Caputo sense. The total domain is discretized into a set of small subdomains and then the unknown functions are approximated using the piecewise Lagrange interpolation polynomial of degree three and degree four. The detailed error analysis is presented, and it is analytically proven that the proposed algorithms are of orders 4 and 5. The stability of the algorithms is rigorously established and the stability region is also achieved. Numerical examples are provided to check the theoretical results and illustrate the efficiency and applicability of the novel algorithms.

【 授权许可】

CC BY