有理逼近和Padé逼近的高阶紧致型方法

HIGH-ORDER COMPACT-TYPE SCHEMES WITH RATIONAL AND PADE APPROXIMATION APPROACHES

对高阶紧致(high order compact)方法进行了详细的讨论和简洁的评述．这就是:回顾了方法的发展历史,指出了方法优点,分析了方法的基本特征、构造方式和应用现状,预示了它的近期发展和研究形势．特别地,就方法的数学基础——有理逼近和Pade逼近进行了归纳．在文章中提供了丰富的方法信息和大量的有关公式．

This paper contains a detailed discussion on the HOC （high order compact） method. The history of the method is reviewed, the strongpoint of the method is pointed out, the basic properties, constructions and its present state are analyzed, together with the recent development. And especially, the mathematical foundations of the HOC-type method are discussed by summing up the relationship between the HOC and the rational approximation or Pad^-type approximations. Moreover, in the paper, rich information and related formulas are provided.