Analysis of a High-Accuracy Numerical Method for Time-Fractional Integro-Differential Equations

Fractal and Fractional

article

Ziyang Luo¹  Xindong Zhang¹  Leilei Wei² 

[1] School of Mathematical Sciences, Xinjiang Normal University;College of Science, Henan University of Technology

关键词: integro-differential equation;    Riemann-Liouville derivative;    high-order approximation;    compact finite difference;    stability;    convergence;   

DOI  :  10.3390/fractalfract7060480

学科分类：社会科学、人文和艺术（综合）

来源: mdpi

【 摘 要 】

A high-order finite difference numerical scheme based on the compact difference operator is proposed in this paper for time-fractional partial integro-differential equations with a weakly singular kernel, where the time-fractional derivative term is defined in the Riemann-Liouville sense. Here, the stability and convergence of the constructed compact finite difference scheme are proved in L ∞ norm, with the accuracy order O (τ 2+h 4), whereτand h are temporal and spatial step sizes, respectively. The advantage of this numerical scheme is that arbitrary parameters can be applied to achieve the desired accuracy. Some numerical examples are presented to support the theoretical analysis.

【 授权许可】

CC BY