Finite Difference Method For Fractional Non-fickian Reaction Diffusion Equations With Variable Coefficient

In this thesis,two kinds of fractional Non-Fickian reaction-diffusion equations with variable coefficients are analyzed.For their initial boundary value problems,the difference schemes are constructed,and the corresponding numerical examples are given.Firstly,around the Non-Fickian time fractional diffusion equation with variable coefficien-t,a difference scheme is obtained by using the L₁ formula to discretize the time Caputo frac-tional derivative,the central difference formula to approximate the second order space partial derivative,and the composite trapezoidal formula to discretize the integral term in the equation,which has 2-order accuracy in time direction,and second order accuracy in spatial direction.The stability and convergence of the difference scheme are proved in detail by using the energy method,and the effectiveness of the difference scheme is verified by numerical examples.Then,for the fractional Non-Fickian delay reaction-diffusion equation with variable co-efficient,a high order difference scheme is obtained by usingL₂-1_? formula to approximate the Caputo fractional derivative.The stability and convergence of the corresponding difference scheme are analyzed and numerically tested.