New lax-friedrichs scheme for convective-diffusion equation

Authors:
Haixin Jiang;Wei Tong
Affiliations:
College of Science, Jiujiang University, Jiujiang, China;College of Science, Jiujiang University, Jiujiang, China
Venue:
ICICA'12 Proceedings of the Third international conference on Information Computing and Applications
Year:
2012

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Abstract

Two different types of generalized Lax-Friedrichs scheme for the convective-diffusion equation ut+aux=εuxx( a∈R, ε0) 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.