101. On the solution of strong nonlinear oscillators by applying a rational elliptic balance method
- Author
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ALEX ELIAS ZUÑIGA, 19150, CIRO ANGEL RODRIGUEZ GONZALEZ, 20794, OSCAR MARTINEZ ROMERO, and 278430
- Subjects
Oscillators (mechanical) ,Duffing equation ,Rational function ,Harmonic balance ,Duffing equations ,Numerical integrations ,Modelling and Simulation ,Jacobi Elliptic function ,Pendulum (mathematics) ,Approximate solution ,Mathematics ,Quarter period ,Non-linear oscillators ,Mathematical analysis ,Elliptic function ,Rational functions ,Nonlinear equations ,Jacobi elliptic functions ,Angular frequencies ,Computational Mathematics ,Nonlinear system ,7 INGENIERÍA Y TECNOLOGÍA ,Computational Theory and Mathematics ,Modeling and Simulation ,Elliptic rational functions ,Rational elliptic forms ,Numerical methods ,Jacobian elliptic functions ,Jacobian elliptic function ,Nonlinear oscillators - Abstract
A rational elliptic balance method is introduced to obtain exact and approximate solutions of nonlinear oscillators by using Jacobi elliptic functions. To illustrate the applicability of the proposed rational elliptic forms in the solution of nonlinear oscillators, we first investigate the exact solution of the non-homogenous, undamped Duffing equation. Then, we introduce first and second order rational elliptic form solutions to obtain approximate solutions of two nonlinear oscillators. At the end of the paper, we compare the numerical integration values of the angular frequencies with approximate solution results, based on the proposed rational elliptic balance method. © 2010 Elsevier Ltd. All rights reserved.
- Published
- 2010
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