High-order compact finite volume scheme for the 2D multi-term time fractional sub-diffusion equation

Advances in Difference Equations

article

Su, Baojin¹  Jiang, Ziwen¹ 

[1] School of Mathematics and Statistics, Shandong Normal University

关键词: 2D multi-term time fractional sub-diffusion equation;    High-order compact finite volume scheme;    Stable;    Convergent;   

DOI  :  10.1186/s13662-020-03128-4

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

Based on an L1 interpolation operator, a new high-order compact finite volume scheme is derived for the 2D multi-term time fractional sub-diffusion equation. It is shown that the difference scheme is unconditionally convergent and stable in$L_{\infty }$ -norm. The convergence order is$O(\tau ^{2-\alpha }+h_{1}^{4}+h_{2}^{4})$ , where τ is the temporal step size and$h_{1}$ is the spatial step size in one direction,$h_{2}$ is the spatial step size in another direction. Two numerical examples are implemented, testifying to their efficiency and confirming their convergence order.

【 授权许可】

CC BY