广义泰勒定理:“同伦分析方法”之有效性的一个数理逻辑证明

廖世俊

广义泰勒定理:“同伦分析方法”之有效性的一个数理逻辑证明

廖世俊

上海交通大学, 船舶及海洋工程学院, 上海, 200030

基金项目: 国家杰出青年基金资助项目(50125923)

详细信息

作者简介:
廖世俊(1963- ),男,教育部"长江奖励计划"特聘教授,博士(E-mail:sjliao@sjtu.edu.cn)

中图分类号: O173.1,O175.14,O189.23
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- 被引次数: 0
出版历程
- 收稿日期: 2002-01-28
- 修回日期: 2002-10-15
- 刊出日期: 2003-01-15

On a Generalized Taylor Theorem:a Rational Proof of the Validity of the So-Called Homotopy Analysis Method

LIAO Shi-jun

School of Naval Architecture & Ocean Engineering, Shanghai Jiaotong University, Shanghai 200030, China

摘要

摘要: 推导了复变函数一个广义意义上的泰勒级数表达式,证明了有关的收敛性定理,大大增大摄动级数解的收敛区域.定理的证明亦为一种新的、求解非线性问题的解析方法(即“同伦分析方法”)的有效性奠定了一个坚实的数理逻辑基础.
- 泰勒级数 /
- 级数之收敛性 /
- 同伦分析方法 /
- 摄动
Abstract: A generalized Taylor series of a complex function was derived and some related theorems about its convergence region were given. The generalized Taylor theorem can be applied to greatly enlarge convergence regions of approximation series given by other traditional techniques. The rigorous proof of the generalized Taylor theorem also provides us with a rational base of the validity of a new kind of powerful analytic technique for nonlinear problems, namely the homotopy analysis method.
- Taylor series /
- convergence and summability of series /
- homotopy analysis method /
- perturbation

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参考文献(17)

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