›› 2014, Vol. 23 ›› Issue (12): 120501-120501.doi: 10.1088/1674-1056/23/12/120501
A generalized Padé approximation method of solving homoclinic and heteroclinic orbits of strongly nonlinear autonomous oscillators
李震波, 唐驾时, 蔡萍
- College of Mechanical and Vehicle Engineering, Hunan University, Changsha 410082, China
A generalized Padé approximation method of solving homoclinic and heteroclinic orbits of strongly nonlinear autonomous oscillators
Li Zhen-Bo (李震波), Tang Jia-Shi (唐驾时), Cai Ping (蔡萍)
- College of Mechanical and Vehicle Engineering, Hunan University, Changsha 410082, China
摘要： 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.
中图分类号: (Computational methods in statistical physics and nonlinear dynamics)
- 05.10.-a