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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

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

Abstract:

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.

Keywords: Precise integration method, Jacobi elliptic function, double periods, singularity, Removable Singularity

DOI:

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