New Lax-Friedrichs scheme for convective-diffusion equation

Abstract

Two different types of generalized Lax-Friedrichs scheme for the convective-diffusion equation u t + au x = εu xx ( a ∈ R, ε > 0) are given and analyzed. For the convection term, both of two schemes use generalized Lax-Friedrichs scheme. For the diffusion term, explicit central difference scheme is used. The propagation of chequerboard mode is considered for two schemes and several numerical examples are presented only for the first scheme , which display how different parameters control oscillations. For low and high frequency modes, applying discrete Fourier analysis , some results have been obtained about stability condition of schemes, and clarify the reasons of oscillations and the interrelation among the amplitude error. © 2012 Springer-Verlag.