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

Supported by National Nature Science Foundation of China and NSF of Shandong Province

Abstract

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

Keywords:

• Parabolic equation
• ADI
• time stepping
• characteristic

Supported by National Nature Science Foundation of China and NSF of Shandong Province

Supported by National Nature Science Foundation of China and NSF of Shandong Province

Notes

Supported by National Nature Science Foundation of China and NSF of Shandong Province