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Zbl 1144.65057
Chen, Chang-Ming; Liu, F.; Burrage, K.
Finite difference methods and a Fourier analysis for the fractional reaction-subdiffusion equation. (English)
[J] Appl. Math. Comput. 198, No. 2, 754-769 (2008). ISSN 0096-3003

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.
[Ruxandra Stavre (Bucureşti)]

MSC 2000:: *65M06 Finite difference methods (IVP of PDE)
65M12 Stability and convergence of numerical methods (IVP of PDE)
35K57 Reaction-diffusion equations

Keywords: space-time fractional derivatives; stability; convergence; fractional reaction-subdiffusion equation; explicit finite difference method; implicit finite difference method; numerical results

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Zentralblatt MATH Berlin [Germany]