Chen, Jinghua An implicit approximation for the Caputo fractional reaction-dispersion equation. (Chinese. English summary) Zbl 1164.65528 J. Xiamen Univ., Nat. Sci. 46, No. 5, 616-619 (2007). Summary: Fractional differential equations can simulate many phenomena contrasting with integer differential equations in lots of applied science. In this paper, a time-fractional reaction-dispersion equation is considered in which the first order derivative is replaced by a Caputo fractional derivative, and an implicit difference scheme is given. Stability and convergence are proved by using the energy method. A numerical example demonstrates that the difference method is effective. Cited in 13 Documents MSC: 65R20 Numerical methods for integral equations 65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs 65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs 35K57 Reaction-diffusion equations 45K05 Integro-partial differential equations 45G10 Other nonlinear integral equations 26A33 Fractional derivatives and integrals Keywords:fractional reaction-dispersion equation; Caputo fractional derivative; difference scheme; stability; convergence; numerical example PDFBibTeX XMLCite \textit{J. Chen}, J. Xiamen Univ., Nat. Sci. 46, No. 5, 616--619 (2007; Zbl 1164.65528)