Finite Difference Methods For Two Dimension Fractional Reaction-subdiffusion Equation

Various fields of science and engineering deal with dynamical systems thatcan be described by fractional partial di?erential equations (FPDE), for exam-ple, systems biology, chemistry and biochemistry applications due to anomalousdi?usion e?ects in constrained environments. However, e?ective numerical meth-ods and numerical analysis for FPDE are still in their infancy. In this paper,we consider a fractional reaction?subdi?usion equation (FR?subDE) in whichboth the motion and the reaction terms are a?ected by the subdi?usive charac-ter of the process. Using the relationship between the Riemann?Liouville andGrunwald?Letnikov definitions of fractional derivatives, an implicit and an ex-plicit di?erence methods for the FR-subDE are presented. The stability and theconvergence of the two numerical methods are investigated by a Fourier anal-ysis. Finally, a comparison between the exact solution and the two numericalsolu- tions is given. The numerical results are in excellent agreement with ourtheoretical analysis.