Two-order Implicit-Explicit BDF Method For Function Differential Equations

This paper is divided into two parts.In the first part,the two-order implicit-explicit BDF method for the initial value problems of composite stiff Volterra functional differential equation is constructed by combining the two-order implicit-explicit BDF method and canonical interpolation operators.Stability,consistency and convergence of numerical method are obtained.Numerical experiments verify that the accuracy of the numerical method is consistent with theoretical results.In the second part,the initial boundary value problems of the two-dimensional R.iesz space fractional diffusion equations are converted into the initial value prob-lems of the nonlinear composite stiff ordinary differential equation by discretiz-ing the spatial variables,furthermore,we apply two-order implicit-explicit BDF method,Canonical Euler splitting method and alternating direction implicit Eu-ler method to solve the above problems.The numerical results show that the proposed two-order implicit-explicit BDF method is effective.