带有爆破现象的反应扩散方程的移动网格方法

A moving mesh method for reaction-diffusion problems with blow-up

研究了带有指数非线性项的反应扩散方程的数值解.针对方程在有限时间内会变得非常奇异,提出了移动网格方法和维数分析方法来解该方程.数值结果验证了当移动网格方程具有等分布占优这个性质的时候,移动网格方法求解方程非常有效.另外,数值结果同样显示了等分布占优不是一个必要条件.

This paper studies the numerical solution of the reaction-diffusion differential equation with an exponential nonlinearity.Since the equation may become singular in a finite time,the moving mesh PDEs method with the dimensional analysis is proposed to solve it.The numerical results show that the moving mesh PDEs method works successfully when the employed moving mesh equation has the dominance of equidistribution.Also,it shows that the dominance of equidistribution is not a necessary condition when the variableτis used.