求解反应扩散问题的Wavelet-Galerkin方法

Wavelet-Galerkin method for the reaction-diffusion equation

提出了一种求解反应扩散问题的小波有限元方法。一般的反应扩散问题都存在着快反应慢扩散的特点,通过渐近分析知道这类问题一般都存在着各种各样的边界层。为了克服由此带来的计算上的困难,结合小波函数的特性,提出了一种自适应的小波有限元算法,不仅可以得到高精度的近似解,与通常的有限元或有限差分方法相比也大大降低了计算复杂度,可以从O(-ε2)降为O1εln1的两个数值例子表明,该方法对于几乎静止和运动的内边界层情形都是非常有效的。

A Wavelet-Galerkin method developed for reaction-diffusion problems. In most such problems, the reaction procedure is much faster than the diffusion procedure and the problems include boundary layers which increase the computational complexity. The usual finite element methods and finite difference methods can not capture the boundary layers exactly with acceptable computational complexity. The self-adapted wavelet method gives high accuracy approximate solutions and reduces the computational complexity from O（ε^-2）to O（1/ε ln 1/ε）. Two numerical examples illustrate the efficiency of the method.