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Duffing equations with cubic and quintic nonlinearities

Pirbodaghi, T ; Sharif University of Technology | 2009

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  1. Type of Document: Article
  2. DOI: 10.1016/j.camwa.2008.10.082
  3. Publisher: 2009
  4. Abstract:
  5. In this study, an accurate analytical solution for Duffing equations with cubic and quintic nonlinearities is obtained using the Homotopy Analysis Method (HAM) and Homotopy Pade technique. Novel and accurate analytical solutions for the frequency and displacement are derived. Comparison between the obtained results and numerical solutions shows that only the first order approximation of the Homotopy Pade technique leads to accurate solution with a maximum relative error less than 0.4%. © 2008 Elsevier Ltd. All rights reserved
  6. Keywords:
  7. Beams and girders ; Control theory ; Analytical solution ; Duffing equations ; Homotopy analysis method ; Homotopy Pade technique ; Quintic nonlinearity ; Control nonlinearities
  8. Source: Computers and Mathematics with Applications ; Volume 57, Issue 3 , 2009 , Pages 500-506 ; 08981221 (ISSN)
  9. URL: https://www.sciencedirect.com/science/article/pii/S0898122108006433