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Rational energy balance method to nonlinear oscillators with cubic term

Daeichin, M ; Sharif University of Technology | 2013

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  1. Type of Document: Article
  2. DOI: 10.1142/S1793557113500198
  3. Publisher: 2013
  4. Abstract:
  5. In this paper, a novel approach is proposed for solving the nonlinear problems based on the collocation and energy balance methods (EBMs). Rational approximation is employed as an initial guess and then it is combined with EBM and collocation method for solving nonlinear oscillators with cubic term. Obtained frequency amplitude relationship is compared with exact numerical solution and subsequently, a very excellent accuracy will be revealed. According to the numerical comparisons, this method provides high accuracy with 0.03% relative error for Duffing equation with strong nonlinearity in the second-order of approximation. Furthermore, achieved results are compared with other types of modified EBMs and the second-order of harmonic balance method. It is demonstrated that the new proposed method has the highest accuracy in comparison with different approaches such as modified EBMs and the second-order of harmonic balance method
  6. Keywords:
  7. Duffing oscillators ; Energy balance method ; Rational approximation
  8. Source: Asian-European Journal of Mathematics ; Volume 6, Issue 2 , 2013 ; 17935571 (ISSN)
  9. URL: http://www.worldscientific.com/doi/abs/10.1142/S1793557113500198