Exact solutions for a nonlinear model

Hernández, Jairo Ernesto Castillo; Salas, Alvaro H.; Lugo, Jose Gonzalo Escobar

doi:10.1016/j.amc.2009.09.011

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Cited by 7 publications

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“…e nonlinear equation describing an oscillator with a cubic nonlinearity is called the Du ng equation. is equation has a variety of applications in science and engineering, early mechanical failure signal, nonlinear circuit design [1], image processing [2], vibration of buckled beams [3], solitons [4][5][6], chaos [7], and many areas of physics.…”

Section: Introductionmentioning

confidence: 99%

The Galerkin Method for Solving Strongly Nonlinear Oscillators

Salas

2022

The Scientific World Journal

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In this paper, we make use of the Galerkin method for solving nonlinear second-order ODEs that are related to some strongly nonlinear oscillators arising in physics and engineering. We derive the iterative schemes for finding the coefficients that appear in the linear Galerkin hat combination in the ansatz form solution. These coefficients may be found iteratively by solving either a quadratic or a higher degree algebraic equation. Examples are presented to illustrate the obtained results. Some exact solutions are given, and they are compared with both the Runge–Kutta numerical solution and the solution obtained using the Galerkin finite element method.

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