L1 Scheme Difference Approximation for Caputo-Hadamard Time Fractional Reaction-Diffusion Equation
A numerical method for solving Caputo-Hadamard time fractional reaction-diffusion equation was presented in this paper.The first order time derivative was replaced by the Caputo-Hadamard derivative and then the Caputo-Hadamard time fractional derivative was approximated by L1 interpolation.The second de-rivative of space was discretized by the central difference formula,and the numerical discretization scheme of the equation was constructed.It was proved that the numerical scheme was stability and convergence.Then Richardson extrapolation was applied to further improve the spatial accuracy,and a specific algorithm was pres-ented to make the new difference scheme reach fourth order convergence in space direction.Finally,a numeri-cal example was implemented to test the efficiency of the numerical scheme.
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