A Spatial Sixth Order Finite Difference Scheme for Time Fractional Sub-diffusion Equation with Variable Coefficient
نویسندگان
چکیده
In this paper, we present a finite difference scheme for a class of time fractional diffusion equation with variable coefficient, where the fractional derivative is defined by the Caputo derivative. The present algorithm is unconditionally stable, and possess spatial sixth order and temporal 2 − α order accuracy, which is an improvement of the spatial fourth order accuracy in the existing results. Theoretical analysis including local truncating error, unique solvability, stability and convergence for this algorithm is fulfilled. Then based on this finite difference scheme, we also investigate the construction of unconditionally stable finite difference scheme for a class of time fractional parabolic equation with spatial fourth derivative. In order to testify the efficiency of the algorithms as well as the convergence orders, some numerical examples are presented.
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