A generalized Padé approximation method of solving homoclinic and heteroclinic orbits of strongly nonlinear autonomous oscillators

doi:10.1088/1674-1056/23/12/120501

Abstract An intrinsic extension of Padé approximation method, called the generalized Padé approximation method, is proposed based on the classic Padé approximation theorem. According to the proposed method, the numerator and denominator of Padé approximant are extended from polynomial functions to a series composed of any kind of function, which means that the generalized Padé approximant is not limited to some forms, but can be constructed in different forms in solving different problems. Thus, many existing modifications of Padé approximation method can be considered to be the special cases of the proposed method. For solving homoclinic and heteroclinic orbits of strongly nonlinear autonomous oscillators, two novel kinds of generalized Padé approximants are constructed. Then, some examples are given to show the validity of the present method. To show the accuracy of the method, all solutions obtained in this paper are compared with those of the Runge–Kutta method.

Keywords: generalized Padé approximation method homoclinic and heteroclinic orbits strongly nonlinear oscillators

Received: 11 April 2014
Revised: 23 July 2014
Accepted manuscript online:

PACS:	05.10.-a	(Computational methods in statistical physics and nonlinear dynamics)
	02.70.-c	(Computational techniques; simulations)
	05.45.-a	(Nonlinear dynamics and chaos)

Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11172093 and 11372102) and the Hunan Provincial Innovation Foundation for Postgraduate, China (Grant No. CX2012B159).

Corresponding Authors: Li Zhen-Bo
E-mail: lizhenbo126@126.com

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Li Zhen-Bo (李震波), Tang Jia-Shi (唐驾时), Cai Ping (蔡萍) A generalized Padé approximation method of solving homoclinic and heteroclinic orbits of strongly nonlinear autonomous oscillators 2014 Chin. Phys. B 23 120501

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A generalized Padé approximation method of solving homoclinic and heteroclinic orbits of strongly nonlinear autonomous oscillators

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