HOMOCLINIC ORBIT OF STRONGLY NONLINEAR AUTONOMOUS OSCILLATOR VIA GENERALIZED PADÉ APPROXIMATION METHOD

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.