同伦分析方法及其在数学中的应用

Homotopy Analysis Method itsApplications in Mathematics

描述了一种新的非线性分析方法，称为“同伦分析方法”的基本思想，引入了一个新的实变函数族，称为趋近函数，给出了该函数族的一些基本性质，并证明，该函数族之函数依次与传统的泰勒级数各项相乘能极大地增大传统泰勒级数的收敛区域。

In this paper, the basic ideas of a new nonlinear analytical technique, namely Homotopy Analysis Method, are described, and a new family of real functions, called approaching functions, is introduced. Some basic properties of this family of real functions are given. It is rigorously proved that the convergence region of the traditional Taylor series can be greatly enlarged by multiplying its each term by ap- proaching functions of this family one after another in order.