DefinePK

Abstract

In this paper we combine the boundary value method (for discretizing the temporal variable) and finite difference scheme (for discretizing the spatial variables) to numerically solve the one dimensional Advection Diffusion Equation. We first employ a fourth order compact scheme to discretize the spatial derivatives. Then a linear system of ordinary differential equation is obtained. Then we apply a fourth order scheme of boundary value method to approach this system. After this, we use the central difference scheme for the temporal variables. Therefore, this scheme can achieve fourth order accuracy for both temporal and spatial variables. Numerical applications are performed to check the correctness and effectiveness of this compact difference scheme, compared with finite difference scheme.