热传导方程求解中的快速小波-有限差分方法

A fast wavelet-finite difference method to solve heat equation

提出了利用小波-有限差分法去求解热传导方程的方法。利用有限差分和紧支集正交小波基对热传导方程的时间、空间变量分别进行离散和变换,将热传导方程的求解转换到小波域中进行,利用小波基的自适应性与消失矩特性,使偏微分算子矩阵稀疏化,与其他方法比较,有效地提高了计算精度.

A fast wavelet - finite difference method is given to solve heat equation, applying the finite difference scheme and the orthonormal compactly supported wavelet transform approximation to the time and the space dimension of the heat equation for discrete and transformation. Equation of heat conduction＇s solution is trans-formed to wavelet, self - adaption and disappeared matrix property, the difference operators have sparseness in the wavelet domain. Comparing to other methods, higher accuracy can be achieved.