A kind of characteristic-splitting method for convection-dominated parabolic equations*

Consider the convection diffusion equations where & is a bounded domain with boundary and a(x) are smooth functions, and . When we use the finite difference or finite element method to solve it, the numerical oscillation will be appear [1]. In this paper we propose a kind of splitting method with time stepping along characteristic for convection diffusion equation, which will be as a kind of high speed algorithm on a sequential computer, and also be implemented on a parallel computer. The maximum principle and the uniform convergence are obtained. We also give the average stability and average error estimates. Finally we give a numerical example