• 论文 •

### 椭圆函数的精细积分改进算法

1. 大连海事大学, 交通与物流工程学院,  工程力学教研室,  辽宁大连~116026
2. 大连理工大学, 运载工程与力学学部工程力学系,   工业装备结构分析国家重点实验室, 辽宁大连~116023
• 出版日期:2008-12-14 发布日期:2008-12-24
• 基金资助:

国家重点基础研究专项经费资助项目(2005CB321704)和国家自然科学基金 (10632030)资助项目.

Yao Zheng, Zhong Wanxie. THE IMPROVED PRECISE INTEGRATION METHOD FOR ELLIPTIC FUNCTIONS[J]. Journal of Numerical Methods and Computer Applications, 2008, 29(4): 251-260.

### THE IMPROVED PRECISE INTEGRATION METHOD FOR ELLIPTIC FUNCTIONS

Yao Zheng,1 Zhong Wanxie2

1. Transportation and Logistics Engineering College , Dalian  Maritime University, Dalian 116026, Liaoning, China
2. Department of Engineering Mechanics, State Key  Laboratory of Structural Analysis for Industrial Equipment,
Dalian University of Technology, Dalian 116024, Liaoning, China
• Online:2008-12-14 Published:2008-12-24

Elliptic functions are a special kind of double period complex functions and are used in engineering widely, especially in nonlinear problems. Many elliptic functions in engineering problems are second order elliptic functions, and many complicated elliptic functions are found to be obtained from second order elliptic functions. The most familiar second order elliptic functions include Jacobi elliptic functions and Weierstrass elliptic functions.  They can be expressed as power series expansion, directly calculating is inconvenient. One of the most important properties of elliptic functions is the additional theorem, so that the method of precise integration can be invoked. Although the precise integration method of elliptic functions has achieved many successes in precision and efficiency, but the singularity problem is still a big enemy of precision. The precise integration method of Jacobi elliptic function is reviewed first. The approximate formulae of removable singularity are educed after analyzing of the singularity. Then the
improved precise integration method is presented based on those formulae and analyses.

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 [1]高本庆. 椭圆函数及其应用[M]. 北京: 国防工业出版社, 1991. [2]Serge Lang. Elliptic Functions-Second Edition [M]. New York: Springer-Verlag, 2003. [3]Keigo, Iizuka. Elements of photonics vol.II-for fiber and integrated optics [M]. New York: John Wiley and Sons Inc, 2002. [4]石顺祥, 陈国夫, 赵卫, 刘继芳. 非线性光学[M]. 西安:西安电子科技大学出版社, 2002. [5]Wanxie Zhong. On precise integration method [J]. Journal of Computational and Applied Mathematics, 2004, 163(1): 59-78. [6]钟万勰. 结构动力方程的精细时程积分法[J]. 大连理工大学学报, 1994, 43(2): 1865-1872. [7]钟万勰. 应用力学对偶体系[M]. 北京: 科学出版社, 2002. [8]钟万勰, 姚征. 椭圆函数的精细积分算法: 应用力学进展[C]. 北京: 科学出版社, 2004: 106-111. [9]Wanxie Zhong, Zheng Yao. The precise integration method for Jacobi elliptic functions and application: Computational Method[C]. Springer, 2006.
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