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

Abstract

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(τ2+h4), where τ and 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.

Keywords

• integro-differential equation
• Riemann-Liouville derivative
• high-order approximation
• compact finite difference
• stability
• convergence