Development and -Analysis of a Single-Step Characteristics Finite Difference Scheme of Second Order in Time for Convection-Diffusion Problems

Abstract

A new finite difference scheme based on the method of characteristics is presented for convection-diffusion problems. The scheme is of single-step and second order in time, and the matrix of the derived system of linear equations is symmetric. Since it is a finite difference scheme, we can get rid of numerical integration which may cause some instability in the characteristics finite element method. An optimal error estimate is proved in the framework of the discrete L 2 -theory. Numerical results are shown to recognize the convergence order and advantages of the scheme.