用多层小波配置法求解热传导方程

Solving Heat Conduct Equations Based on Multilevel Wavelet Collocation Method

以热传导方程为例,提出一种求解偏微分方程的多层插值小波配置法,利用Shannon尺度函数的插值特性构造了多层插值的尺度基函数,从而实现了对偏微分方程的空间离散,建立了关于时间的常微分方程组,然后采用Runge-Kutta法对该方程组求解.最后给出算例,说明了此算法的有效性和较高的精确度.

A multilevel wavelet collocation method is used for the solution of partial differential equations.Based on the interpolation property of Shannon wavelet,the multilevel Shannon basis is structured;so the system of ordinary differential equation to time was built.Then the Runge-Kutta method is used to solve the system of equations.With the computational precision of the method,the numerical example indicates that the method is accurate and efficient.