时间分数阶变系数对流扩散方程的数值解法

doi:10.3976/j.issn.1002-4026.2020.01.016

Abstract

Abstract: Most studies of convection-diffusion equation are in the range of constant coefficient or integer order. To more accurately describe the solute movement features, the traditional integer order convection-diffusion equation is extended to cases of fractional order variable coefficient. The paper primarily investigated the finite difference decomposition method of Caputo fractional order convection-diffusion equation with variable coefficients. This paper introduced a half integer point, performed dual partitioning on the spatial grid,and then discretized the spatial derivatives using the finite difference method. Theoretical analysis shows that the solution of the discrete format proposed in this paper exists and is unique, with a convergence accuracy of ο(τ+h).The accuracy of theoretical analysis is verified using one-dimensional numerical examples.

Key words: fractional order, convection-diffusion equation, finite difference method, stability, convergence

CLC Number:

O241.82

GUO Fei-fan, ZHANG Xin-dong, WANG Shuo. Numerical solution for convection-diffusion equation with time fractional variable coefficients[J].Shandong Science, 2020, 33(1): 116-123.

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Numerical solution for convection-diffusion equation with time fractional variable coefficients

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