An alternating direction Galerkin method for a time-fractional partial differential equation with damping in two space dimensions

Advances in Difference Equations

An Chen¹  Changpin Li² 

[1] College of Science, Guilin University of Technology;Department of Mathematics, Shanghai University;

关键词: ADI Galerkin method;    Caputo derivative;    unconditional stability;    convergence;   

DOI  :  10.1186/s13662-017-1414-9

来源: DOAJ

【 摘 要 】

Abstract In this paper, we propose an efficient alternating direction implicit (ADI) Galerkin method for solving the time-fractional partial differential equation with damping, where the fractional derivative is in the sense of Caputo with order in ( 1 , 2 ) $(1,2)$ . The presented numerical scheme is based on the L2- 1 σ $1_{\sigma}$ method in time and the Galerkin finite element method in space. The unconditional stability and convergence of the numerical scheme are both carefully proved. Numerical results are displayed for supporting the theoretical analysis.

【 授权许可】

Unknown