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Symbolic computation of strongly nonlinear periodic oscillations. (English) Zbl 1325.68292

Summary: Based on Wu’s elimination method and homotopy analysis method (HAM), an algorithm is proposed to compute accurate analytic approximation of periodical oscillations with high nonlinearity. A Maple package is developed for periodically oscillating systems of center and limit cycle types, which delivers accurate approximations of frequency, mean of motion and amplitude of oscillation automatically. Since HAM is valid for highly nonlinear problems, the package can be used to find accurate approximate solutions of nonlinear oscillation systems with strong nonlinearity. For systems with physical parameters, it can provide possible constraint conditions on parameters. Several examples are given to illustrate the validity and effectiveness of the algorithm and the Maple package. This package is freely available online, which provides an easy-to-use tool for scientist and engineer to solve accurate approximations of periodic oscillations of dynamic systems with high nonlinearity.

MSC:

68W30 Symbolic computation and algebraic computation
65L99 Numerical methods for ordinary differential equations
68T15 Theorem proving (deduction, resolution, etc.) (MSC2010)
34C15 Nonlinear oscillations and coupled oscillators for ordinary differential equations

Software:

Maple; BVPh; MEDLAR; Epsilon
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References:

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