The Implicit Perturbation Difference Scheme Of Convection Diffusion Equation

In this paper, a high order accuracy difference method is presented for solving unsteady convection diffusion equation by using Implicit Perturbation Finite Difference (IPFD) scheme. Firstly, we use the steady convection diffusion equation, the constant coefficients of this equation are expanded to power series of grid-spacings, then the high-order Perturbation Finite Difference (PFD) scheme is obtained by determining the coefficients of the power series. Put this scheme on unsteady convection diffusion equations and modified it, the IPFD scheme is constructed. Secondly, we handle unsteady convection diffusion equation directly, the coefficients of this equation are expanded to power series of grid-spacings of both time and space, upon that we get the high order time and space accuracy IPFD scheme, this scheme not only remain the terse form of first-order upwind scheme, but also have one time step with three order accurate and essentially non-oscillatory property. Thirdly, we use Fourier and energy method to proof the stable, convergence and TVD ability of IPFD scheme. Endly, the accuracy and resolution of this scheme are numerially examined by using several model equations and get well results.