三次样条小波插值解偏微分方程(英文)

Cubic Spline Wavelet Interpolation and PDE

提出一种在sobolev空间解偏微分方程的三次样条小波插值法.多分辨分析和网格之间存在着某种相似性,从而在有限差分意义下,插值函数与网格剖分之间有联系.利用此性质本文建立了一个解偏微分方程的相关式.最后的数值例子证明了所建相关式的有效性,即证明了所提插值法的有效性.

In this paper, we present a cubic spline wavelet interpolating approach in a sobolev space to solve elliptic boundary value problems which encountered in mathematics physics. Since there are some similarities between multiresolution analysis （MRA） and multigrid scheme, the interpolating function and mesh division depend on each other in the sense of difference scheme. We construct a relative formula to solve concrete PED by means of using this property. Numerical example LUustrates the validity of this new method.