Modified implicit fractional difference scheme for 2D modified anomalous fractional sub-diffusion equation

Advances in Difference Equations

Syed Tauseef Mohyud-Din¹  Umair Ali²  Farah Aini Abdullah² 

[1] Department of Mathematics, HITEC University, Taxila Cantt, Pakistan;School of Mathematical Sciences, Universiti Sains Malaysia, Pulau Pinang, Malaysia

关键词: modified anomalous fractional sub-diffusion equation;    modified implicit difference method;    stability;    convergence;   

DOI  :  10.1186/s13662-017-1192-4

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we solve two-dimensional modified anomalous fractional sub-diffusion equation using modified implicit finite difference approximation. The stability and convergence of the proposed scheme are analyzed by the Fourier series method. We show that the scheme is unconditionally stable and the approximate solution converges to the exact solution. A numerical example is given to show the application and feasibility of the proposed scheme.

【 授权许可】

CC BY