Approximate methods based on order reduction for the periodic solutions of nonlinear third-order ordinary differential equations

DOI10.1016/j.amc.2009.12.057zbMath1186.65091OpenAlexW2051233168MaRDI QIDQ961628

Juan I. Ramos

Publication date: 31 March 2010

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2009.12.057

zbMATH Keywords

periodic solutionsoscillationnumerical examplesartificial parameterorder reductionjerk dynamicsthird-order nonlinear ordinary differential equationsLinstedt-Poincaré method

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Nonlinear ordinary differential equations and systems (34A34) Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations (34C10) Numerical methods for initial value problems involving ordinary differential equations (65L05)

Related Items (6)

Comparison of two iteration procedures for a class of nonlinear jerk equations ⋮ Improvement of Analytical Solution to the Inverse Truly Nonlinear Oscillator by Extended Iterative Method ⋮ Periodic orbits of the fourth-order non-autonomous differential equation \(u'+qu+pu=\varepsilon F(t,u,u',u,u)\) ⋮ On two classes of autonomous third-order nonlinear ordinary differential equations ⋮ Acoustic radiation force on a sphere in standing and quasi-standing zero-order Bessel beam tweezers ⋮ A Volterra integral formulation for determining the periodic solutions of some autonomous, nonlinear, third-order ordinary differential equations

Cites Work

• Perturbation method for periodic solutions of nonlinear jerk equations
• On nonlinear dynamical systems topologically conjugate to jerky motion via a linear transformation
• Elementary chaotic flow
• Simplest dissipative chaotic flow.
• Harmonic balance approach to periodic solutions of non-linear jerk equations
• Harmonic balance approach to limit cycles for nonlinear jerk equations
• Non-chaotic behaviour in three-dimensional quadratic systems
• Perturbation methods and non-linear hyperbolic waves
• Nonchaotic behaviour in three-dimensional quadratic systems II. The conservative case

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