Author(s)

Peng Zhu¹, Shenglan Xie²

¹Department of Mathematics, Jiaxing University, Jiaxing, China.
²Nanhu College, Jiaxing University, Jiaxing, China.

In this paper, an alternating direction Galerkin finite element method is presented for solving 2D time fractional reaction sub-diffusion equation with nonlinear source term. Firstly, one order implicit-explicit method is used for time discretization, then Galerkin finite element method is adopted for spatial discretization and obtain a fully discrete linear system. Secondly, Galerkin alternating direction procedure for the system is derived by adding an extra term. Finally, the stability and convergence of the method are analyzed rigorously. Numerical results confirm the accuracy and efficiency of the proposed method.

Nonlinear Fractional Differential Equation, Alternating Direction Implicit Method, Finite Element Method, Riemann-Liouville Fractional Derivative

Zhu, P. and Xie, S. (2016) ADI Finite Element Method for 2D Nonlinear Time Fractional Reaction-Subdiffusion Equation. American Journal of Computational Mathematics, 6, 336-356. doi: 10.4236/ajcm.2016.64034.