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An implicit approximation for the Caputo fractional reaction-dispersion equation. (Chinese. English summary) Zbl 1164.65528

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.

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
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