對流擴散方程的數值爆炸問題

Numerical Blow-up Problems for a Convective Reaction-diffusion Equation

吳依蒨(Yi-Chien Wu)

指導教授 ： 卓建宏

國立中正大學/理學院/數學系研究所/碩士(2014年)

摘要

考慮一個對流擴散方程u_t=u_{xx}+alpha(u^m)_x+u^{eta}, (0< x< 1,~ 0m>=1 去探討它的數值爆炸問題以及解的收斂性

關鍵字

數值爆炸問題 ； 對流擴散方程

並列摘要

We consider a finite difference scheme for the convective reaction-diffusion equation $u_t=u_{xx}+alpha(u^m)_x+u^{eta}, (0< x< 1,~ 0mgeqslant 1$ and $alpha>0$ are parameters. For many differential equations or systems the solutions can become unbounded in finite time $T$. Here the phenomena that is known as blow-up and the finite time $T$ is called the blow-up time. In this paper, we prove that the numerical blow-up time converges to the blow-up time with uniform temporal grid size.

並列關鍵字

Convective Reaction-diffusion Equation ； Numerical Blow-up Problems

參考文獻

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