两点边值问题的小波配点法

根据多分辨分析,提出用任意连续的尺度函数构造区间上的插值基函数,形成以尺度函数为基础的求解两点边值问题的小波配点法.该方法中,尺度函数不受紧支撑、插值等性质的限制,计算复杂度小,数值解收敛性由多分辨分析理论保证.同时,给出边值条件的积分处理方法,能够方便地处理任意边界条件,当尺度函数不具有高阶导数时,该方法也能有效使用.数值算例表明,该方法是一个高效、高精度的算法.

A wavelet collocation method for solving two-point boundary value problems

Based on multi-resolution analysis,a wavelet collocation method of solving two-point boundary value problem using sealing function is proposed in this paper. The interpolation base functions in interval of the collocation method are formed by using arbitrary continuous scaling function,but the scaling function itself dose not required the properties of compact support,interpolation and so on. The computational complexity of this method is low,and the convergence is ensured by multi-resolution analysis theory. At the same time,an integral approach of dealing with boundary condition is suggested,which can handle arbitrary boundary condition conveniently. As the scaling function has no high-order derivative,the method can be used effectively. Numerical example indicates that the method is a highly efficient and accurate algorithm.