High-order Compact Difference Schemes for the Modified Anomalous Subdiffusion Equation

TL;DR

This paper develops high-order compact finite difference schemes for the fractional anomalous subdiffusion equation, achieving high convergence orders and validating their effectiveness through numerical experiments.

Contribution

It introduces two novel high-order compact difference schemes for fractional derivatives, with detailed stability, solvability, and convergence analysis.

Findings

Convergence orders of D7;2+h^6 and D7;2+h^8 achieved.

Numerical experiments confirm theoretical convergence and stability.

New schemes improve accuracy for fractional subdiffusion equations.

Abstract

In this paper, two kinds of high-order compact finite difference schemes for second-order derivative are developed. Then a second-order numerical scheme for Riemann-Liouvile derivative is established based on fractional center difference operator. We apply these methods to fractional anomalous subdiffusion equation to construct two kinds of novel numerical schemes. The solvability, stability and convergence analysis of these difference schemes are studied by Fourier method in details. The convergence orders of these numerical schemes are $\mathcal {O}(\tau^2+h^6)$ and $\mathcal {O}(\tau^2+h^8)$, respectively. Finally, numerical experiments are displayed which are in line with the theoretical analysis.