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Finite difference methods and a Fourier analysis for the fractional reaction-subdiffusion equation. (English) Zbl 1144.65057
This paper deals with a fractional reaction-subdiffusion equation (FR-subDE) in a bounded domain in which both the motion and the reaction terms are affected by the subdiffusive character of the process. An implicit finite difference method (IFDM) and an explicit finite difference method (EFDM) for the FR-subDE are proposed. The stability and the convergence of the IFDM and EFDM are discussed using a Fourier analysis and the solvability of the IFDM is proved. A comparison between the exact solution and the two numerical solutions shows the agreement of the theoretical analysis with the numerical results.
MSC:
65M06Finite difference methods (IVP of PDE)
65M12Stability and convergence of numerical methods (IVP of PDE)
35K57Reaction-diffusion equations