无界区域问题的谱和拟谱方法 献给林群教授80华诞  

Spectral and pseudospectral methods for unbounded domains

作　　者：郭本瑜[1,2,3] 

机构地区：[1]上海师范大学数理学院,上海200234 [2]上海高校科学计算重点实验室,上海200234 [3]上海高校计算科学E-研究院,上海200234

出　　处：《中国科学：数学》2015年第7期975-1024,共50页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:11171227);教育部博士点基金(批准号:20123127110001);上海高校E-研究院基金(批准号:E03004);上海市教育委员会重点学科建设(批准号:J50101)资助项目

摘　　要：本文综述无界区域问题和外部问题谱及拟谱方法的研究成果和最新发展趋势.第一类数值方法基于应用Hermite多项式和函数及Laguerre多项式和函数的正交逼近和插值理论.第二类数值方法基于经过适当变量变换的Jacobi正交逼近和插值理论.第三类数值方法是上述正交逼近和插值方法与区域分解等其他方法的各种组合.本文还总结了Hermite、Laguerre和Jacobi无理正交逼近和插值理论的主要结果,它们是有关数值方法的理论基础.In this paper, we review the current trends and progresses in spectral and pseudospectral methods for unbounded domains and exterior problems. The first kind of numerical methods are based on the orthogonal approximations and interpolations by using the Hermite polynomials and functions, and the Laguerre polynomi- als and functions. The second kind of numerical methods are based on the Jacobi orthogonal approximations and interpolations with suitable variable transformations. The third kind of numerical methods are induced by the various combinations of the previous orthogonal approximations and interpolations coupled with domain decomposition and other techniques. We also present the main results on the Hermite, Laguerre, Jacobi irra- tional orthogonal approximations and interpolations, which serve as the mathematical foundation of the related numerical algorithms.

关 键 词：谱和拟谱方法 无界区域上的微分方程 外部问题 

分 类 号：O241.82[理学—计算数学]