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Asymptotic numerical method for multi-degree-of-freedom nonlinear dynamic systems. (English) Zbl 1136.65117

Summary: The homotopy perturbation method proposed by J. He [Commun. Nonlinear Sci. Numer. Simul. 3, No. 2, 92–97 (1998; Zbl 0921.35009); Commun. Nonlinear Sci. Numer. Simul. 3, No. 2, 106–109 (1998; Zbl 0918.65034)] is very effective and convenient for single-degree-of-freedom systems. In this paper a coupling technique of He’s method and precise integration method (PIM) is suggested to solve multi-degree-of-freedom nonlinear dynamic systems. The new technique keeps the merits of the two methods. Some examples are given to illustrate its effectiveness and convenience. Furthermore the obtained solution is of high accuracy.

MSC:

65P10 Numerical methods for Hamiltonian systems including symplectic integrators
37M15 Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems

Software:

Matlab
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References:

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