Recent developments of the Sinc numerical methods
Recent developments of the Sinc numerical methods
复制标题
DOI：
10.1016/j.cam.2003.09.016
复制
发表时间：
2004-03
影响因子：
2.4
通讯作者：
M. Sugihara;Takayasu Matsuo
中科院分区：
文献类型：
--
作者：
M. Sugihara;Takayasu Matsuo
本文综述了 Sinc 数值方法的最新发展。 Stenger 和他的学校开发了多种 Sinc 数值方法。对于某一类问题，Sinc 数值方法的收敛速度为 O ( exp (−κ n ))，其中 κ>0，其中 n 是方法中使用的节点或基数。最近发现，对于较小但仍然具有实际意义的一类问题，Sinc 数值方法可以实现 O ( exp (−κ′n/ log n)) 的收敛速度，且某些 κ′>0，并且这些收敛速度是最好的。本文证明了两种 Sinc 数值方法的这些事实：两点边值问题的 Sinc 近似和 Sinc 搭配方法。
This paper gives a survey of recent developments of the Sinc numerical methods. A variety of Sinc numerical methods have been developed by Stenger and his school. For a certain class of problems, the Sinc numerical methods have the convergence rates of O ( exp (−κ n )) with some κ>0, where n is the number of nodes or bases used in the methods. Recently it has turned out that the Sinc numerical methods can achieve convergence rates of O ( exp (−κ′n/ log n)) with some κ′>0 for a smaller but still practically meaningful class of problems, and that these convergence rates are best possible. The present paper demonstrates these facts for two Sinc numerical methods: the Sinc approximation and the Sinc-collocation method for two-point boundary value problems.