A novel ADI Galerkin spectral element method for the solution of two-dimensional time fractional subdiffusion equation

Abstract

In this paper, a new numerical technique is presented for the solution of two-dimensional time fractional subdiffusion equation. To this end, we use the Galerkin spectral element method to discretize the spatial derivatives, weighted and shifted Grünwald difference (WSGD) operator to discretize the fractional term and for the time stepping, an alternating direction implicit (ADI) method based on the Crank-Nicolson scheme is investigated. The unconditionally stability of the proposed method as well as an error estimate for the full discretization scheme are presented. Numerical results are reported to support the theoretical analysis and to show the accuracy and efficiency of proposed method in comparison with other ADI schemes.

Keywords:

• Time fractional sub-diffusion equation
• alternating direction implicit
• unconditionally stable
• error estimate
• Legendre Galerkin spectral element method

2010 Mathematics Subject Classifications:

• 65M06
• 65M12
• 65M60

Disclosure statement

No potential conflict of interest was reported by the author(s).