✦ LIBER ✦

Higher order approximate periodic solutions for nonlinear oscillators with the Hamiltonian approach

✍ Scribed by A. Yildirim; Z. Saadatnia; H. Askari; Y. Khan; M. KalamiYazdi

Publisher: Elsevier Science
Year: 2011
Tongue: English
Weight: 720 KB
Volume: 24
Category: Article
ISSN: 0893-9659
DOI: 10.1016/j.aml.2011.05.040

No coin nor oath required. For personal study only.

✦ Synopsis

In this work, the Hamiltonian approach is applied to obtain the natural frequency of the Duffing oscillator, the nonlinear oscillator with discontinuity and the quintic nonlinear oscillator. The Hamiltonian approach is then extended to the second and third orders to find more precise results. The accuracy of the results obtained is examined through time histories and error analyses for different values for the initial conditions. Excellent agreement of the approximate frequencies and the exact solution is demonstrated. It is shown that this method is powerful and accurate for solving nonlinear conservative oscillatory systems.

📜 SIMILAR VOLUMES

The approximate solution of steady tempe

The approximate solution of steady temperature distribution in a rod: Two-point boundary value problem with higher order nonlinearity

✍ Ali Konuralp 📂 Article 📅 2010 🏛 Elsevier Science 🌐 English ⚖ 280 KB

Analytical studies of the steady solutio

Analytical studies of the steady solution for optical soliton equation with higher-order dispersion and nonlinear effects

✍ Chang Lin; Xue-ren Hong; Fu-quan Dou 📂 Article 📅 2008 🏛 Elsevier Science 🌐 English ⚖ 160 KB

The exact analytical solution of the optical soliton equation with higher-order dispersion and nonlinear effects has been obtained by the method of separating variables. The new type of optical solitary wave solution, which is quite different from the bright and dark soliton solutions, has been foun

Explicit eighth order methods for the nu

Explicit eighth order methods for the numerical integration of initial-value problems with periodic or oscillating solutions

✍ T.E. Simos 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 740 KB

New approach for the existence of pseudo

New approach for the existence of pseudo almost periodic solutions for some second order differential equation with piecewise constant argument

✍ Elhadi Ait Dads; Lahcen Lhachimi 📂 Article 📅 2006 🏛 Elsevier Science 🌐 English ⚖ 181 KB

Existence and approximation of solutions

Existence and approximation of solutions for first-order discontinuous difference equations with nonlinear global conditions in the presence of lower and upper solutions

✍ A. Cabada; V. Otero-Espinar; R.L. Pouso 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 756 KB

This paper is devoted to the study of the existence of solutions of first-order difference equations verifying nonlinear conditions that involve the global behavior of the solution. We prove that the existence of lower and upper solutions warrants the existence of such solutions lying in the sector