Orthogonal spline collocation method for the two-dimensional fractional sub-diffusion equation

Authors:
Xuehua Yang;Haixiang Zhang;Da Xu
Affiliations:
Department of Mathematics, Hunan Normal University, 410081 Changsha, PR China;School of Mathematics, Central South University, 410075 Changsha, PR China;Department of Mathematics, Hunan Normal University, 410081 Changsha, PR China
Venue:
Journal of Computational Physics
Year:
2014

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Abstract

The aim of this paper is to develop a novel numerical techniques for the solution of the two-dimensional fractional sub-diffusion equation. The proposed technique is based on orthogonal spline collocation (OSC) method in space and a finite difference method (FDM) in time. Stability and convergence of the proposed method are rigorously discussed and theoretically proven. We present the results of numerical experiments in one and two space variables, which confirm the predicted convergence rates and exhibit optimal accuracy in various norms.