HOMOCLINIC ORBIT OF STRONGLY NONLINEAR AUTONOMOUS OSCILLATOR VIA GENERALIZED PADÉ APPROXIMATION METHOD
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摘要: 在经典Padé逼近理论的基础上进行了相应推广,提出了广义Padé逼近方法,并针对强非线性自治振子同宿轨的求解问题,利用双曲函数构造了一种新的广义Padé逼近式. 首先,该广义Padé逼近式有着较简单的泰勒展开式,与现有的Padé逼近式相比,在计算同阶逼近时,计算量更少;其次,该方法在强非线性时,依然有着较高的精度;第三,该方法并不局限于某些特定的系统,而是有着较广的适用范围. 因此对于广义Padé逼近方法的研究具有一定的实际意义和理论价值.Abstract: The generalized Padé approximate definition is proposed based on classical definition of Padé approximation. By utilizing the hyperbolic function, a new form of generalized Padé approximation is constructed for determining the homoclinic orbit of strongly nonlinear autonomous oscillator. The Taylor expansion of generalized Padé approximation in this paper is simpler than existing ones, which means that the proposed method has less complexity in calculation. The precision of the solutions is high when the nonlinear parameters are large. The proposed method is not restricted to solve some certain systems. It can be utilized in many kinds of systems, which means that the proposed method is generally applicable. So the investigation in generalized Padé approximation is meaningful.
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Key words:
- generalized Padé /
- approximate /
- homoclinic orbit /
- strongly nonlinear
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