Duffing equations with cubic and quintic nonlinearities

• Published in: Computers & mathematics with applications (1987) Vol. 57; no. 3; pp. 500 - 506
• Main Authors: Pirbodaghi, T., Hoseini, S.H., Ahmadian, M.T., Farrahi, G.H.
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.02.2009
• Subjects: Analytical solution; Approximation; Computer simulation; Displacement; Duffing equation; Duffing equations; Ham; Homotopy analysis method; Homotopy Pade technique; Mathematical analysis; Mathematical models; Nonlinearity; Quintic nonlinearity; Duffing equations; Quintic nonlinearity; Homotopy Pade technique; Analytical solution; Homotopy analysis method
• ISSN: 0898-1221; 1873-7668
• DOI: 10.1016/j.camwa.2008.10.082

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%.