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

作者：Ding, Hengfei^*; Li, Changpin

来源：Numerical Methods for Partial Differential Equations, 2016, 32(1): 213-242.

DOI：10.1002/num.21992

• Fourier method
• Grunwald-Letnikov derivative
• high-order compact difference schemes
• modified anomalous subdiffusion equation
• Riemann-Liouville derivative

In this article, two kinds of high-order compact finite difference schemes for second-order derivative are developed. Then a second-order numerical scheme for a Riemann-Liouvile derivative is established based on a fractional centered difference operator. We apply these methods to a 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 using Fourier method. The convergence orders of these numerical schemes are O(tau(2) + h(6)) and O(tau(2) + h(8)), respectively. Finally, numerical experiments are displayed which are in line with the theoretical analysis.

• 出版日期2016-1
• 单位天水师范学院; 上海大学