Quintication method to obtain approximate analytical solutions of non-linear oscillators

被引：26

作者：

Escuela Nacional de Posgrado en Ciencias, Ingenieria y Tecnologias, Tecnologico de Monterrey, Campus Monterrey, E. Garza Sada 2501, Sur, C.P. 64849 Monterrey, N.L., Mexico ^{[1
]}

机构：

来源：

Appl. Math. Comput. | / 849-855期

关键词：

Oscillators (mechanical) - Nonlinear equations - Ordinary differential equations - Polynomials;

D O I：

10.1016/j.amc.2014.05.085

中图分类号：

学科分类号：

摘要：

In this paper we propose a new approach to replace nonlinear ordinary differential equations by approximate cubic-quintic Duffing oscillators in which its coefficients depend on the initial amplitude of oscillation. It is shown that this procedure leads to angular frequency values with relative errors that are lower than those found by previously developed approximate solutions. © 2014 Elsevier Inc. All rights reserved.

引用

共 50 条

[1] APPROXIMATE ANALYTIC SOLUTIONS FOR SINGULAR NON-LINEAR OSCILLATORS
BOTA, KB
MICKENS, RE
[J]. JOURNAL OF SOUND AND VIBRATION, 1984, 96 (02) : 277 - 279
[2] Invariants and approximate solutions for certain non-linear oscillators by means of the field method
Kovacic, Ivana
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2010, 215 (09) : 3482 - 3487
[3] An analytical approximate technique for a class of strongly non-linear oscillators
Wu, B. S.
Sun, W. P.
Lim, C. W.
[J]. INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS, 2006, 41 (6-7) : 766 - 774
[4] APPROXIMATE ANALYTICAL SOLUTIONS TO NON-LINEAR STEERING EQUATIONS.
Flower, J.O.
[J]. 1600, (21):
[5] An approximate method to obtain the fundamental solution for non-linear hyperelastic materials
Prieto, I
Lorenzana, A
Garrido, JA
[J]. BOUNDARY ELEMENTS XIX, 1997, : 689 - 698
[6] Approximate method to obtain the fundamental solution for non-linear hyperelastic materials
Prieto, I.
Lorenzana, A.
Garrido, J.A.
[J]. 1997,
[7] Energy Method to Obtain Approximate Solutions of Strongly Nonlinear Oscillators
Elias-Zuniga, Alex
Martinez-Romero, Oscar
[J]. MATHEMATICAL PROBLEMS IN ENGINEERING, 2013, 2013
[8] Solutions of non-linear oscillators by the modified differential transform method
Momani, Shaher
Ertuerk, Vedat Suat
[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2008, 55 (04) : 833 - 842
[9] ANALYTICAL APPROXIMATE SOLUTIONS OF THE NON-LINEAR BASIC EQUATIONS IN CLASSICAL PHYSICS
MINELLI, TA
PUSTERLA, M
ROBERTY, NC
[J]. LETTERE AL NUOVO CIMENTO, 1980, 27 (11): : 331 - 335
[10] APPROXIMATE ANALYTICAL SOLUTIONS OF NON-LINEAR LOCAL FRACTIONAL HEAT EQUATIONS
Deng, Shuxian
[J]. THERMAL SCIENCE, 2019, 23 : S837 - S841

← 1 2 3 4 5 →