On Linstedt-Poincaré techniques for the quintic Duffing equation
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Publication:990597
DOI10.1016/j.amc.2007.03.050zbMath1193.65142OpenAlexW1976341105MaRDI QIDQ990597
Publication date: 1 September 2010
Published in: Applied Mathematics and Computation (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.amc.2007.03.050
Perturbations of ordinary differential equations (34D10) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Perturbations, asymptotics of solutions to ordinary differential equations (34E10)
Related Items (21)
Solution of the damped cubic-quintic Duffing oscillator by using Jacobi elliptic functions ⋮ A non-iterative derivative-free method for nonlinear ordinary differential equations ⋮ A new perturbation technique in solution of nonlinear differential equations by using variable transformation ⋮ Periodic solutions for certain non-smooth oscillators by iterated homotopy perturbation method combined with~modified Lindstedt-Poincaré technique ⋮ Perturbation-iteration method for first-order differential equations and systems ⋮ Exact solution for the unforced Duffing oscillator with cubic and quintic nonlinearities ⋮ An accurate closed-form approximate solution for the quintic Duffing oscillator equation ⋮ Periodic solutions for Hamiltonian equation associated with Gaussian potential ⋮ Application of modified Mickens iteration procedure to a pendulum and the motion of a mass attached to a stretched elastic wire ⋮ Bifurcations and chaos in Duffing equation with damping and external excitations ⋮ Notes on ``Application of the Hamiltonian approach to nonlinear oscillators with rational and irrational elastic terms ⋮ Piecewise homotopy methods for nonlinear ordinary differential equations ⋮ On the variational iteration method and other iterative techniques for nonlinear differential equations ⋮ Computation of periodic solutions in perturbed second-order ODEs ⋮ Uniform global asymptotic stability for oscillators with nonlinear damping and nonlinear restoring terms ⋮ Linearized Galerkin and artificial parameter techniques for the determination of periodic solutions of nonlinear oscillators ⋮ Analytical approximate solutions for the cubic-quintic Duffing oscillator in terms of elementary functions ⋮ Explicit and exact solutions to cubic Duffing and double-well Duffing equations ⋮ Analytical approximate solutions for conservative nonlinear oscillators by modified rational harmonic balance method ⋮ Nonlinear oscillator with discontinuity by generalized harmonic balance method ⋮ Closed-form exact solutions for the unforced quintic nonlinear oscillator
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