Duffing equations with cubic and quintic nonlinearities.

*(English)*Zbl 1165.34310Summary: 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 PadĂ© 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%.

##### MSC:

34A45 | Theoretical approximation of solutions to ordinary differential equations |

##### Keywords:

Duffing equations; quintic nonlinearity; analytical solution; homotopy analysis method; homotopy pade technique
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\textit{T. Pirbodaghi} et al., Comput. Math. Appl. 57, No. 3, 500--506 (2009; Zbl 1165.34310)

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##### References:

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