| 摘要: |
| 提出对流扩散方程ut+aux=εuxx,a∈R,ε>0的广义Lax-Friedrichs格式(GLxF),并给出GLxF格式的稳定与收敛条件.然后通过数值仿真说明GLxF格式数值解存在振荡,并根据仿真结果提出振荡可控的3个猜测.最后用Fourier分析方法证明了GLxF格式数值解振荡的可控性. |
| 关键词: 对流扩散方程 GLxF格式 振荡 可控性 Fourier分析 |
| DOI： |
| 投稿时间：2010-11-02修订日期：2011-01-17 |
| 基金项目: |
|
| The Controllability of Oscillations in Numerical Solutions of GLxF Scheme for Convective-diffusion Equation |
|
SHEN Liu-ping
|
| (Department of Mathematics and Computer Science, Liuzhou Teachers College, Liuzhou, Guangxi, 545004, China) |
| Abstract: |
| GLxF scheme of convective-diffusion equation ut+aux=εuxx, a∈R, ε>0, is proposed, and its stability and convergence conditions is presented.Then the behavior of numerical solution of GLxF scheme is simulated.The results show that there are oscitlations, of which three guesses of controllability are proposed.Finally, Fourier analysis is used to prove that the oscillations of numerical solution are controllable. |
| Key words: convective-diffusion equation GLxF scheme oscillations controllability Fourier analysis |
