Determination of natural frequencies by coupled method of homotopy perturbation and variational method for strongly nonlinear oscillators

In this paper a new approach combining the features of the homotopy concept with variational approach is proposed to find accurate analytical solutions for nonlinear oscillators with and without a fractional power restoring force. Since the first-order approximation leads to very accurate results, c...

Full description

Saved in:
Bibliographic Details
Published in:Journal of mathematical physics 2011-02, Vol.52 (2), p.023518-023518-10
Main Authors: Akbarzade, M., Langari, J.
Format: Article
Language:English
Subjects:
Accuracy
ANALYTICAL SOLUTION
Approximation
APPROXIMATIONS
CALCULATION METHODS
Comparative analysis
COMPARATIVE EVALUATIONS
DIFFERENTIAL EQUATIONS
ELECTRONIC EQUIPMENT
EQUATIONS
EVALUATION
Exact sciences and technology
Frequencies
HARMONIC OSCILLATORS
Mathematical analysis
MATHEMATICAL METHODS AND COMPUTING
Mathematical methods in physics
Mathematical problems
MATHEMATICAL SOLUTIONS
Mathematics
NONLINEAR PROBLEMS
OSCILLATORS
PERTURBATION THEORY
Physics
Sciences and techniques of general use
Validity
VARIATIONAL METHODS
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper a new approach combining the features of the homotopy concept with variational approach is proposed to find accurate analytical solutions for nonlinear oscillators with and without a fractional power restoring force. Since the first-order approximation leads to very accurate results, comparisons with other results are presented to show the effectiveness of this method. The validity of the method is independent of whether or not there exist small or large parameters in the considered nonlinear equations; the obtained results prove the validity and efficiency of the method, which can be easily extended to other strongly nonlinear problems. At the end we compare our procedure with the optimal homotopy perturbation method.
ISSN:0022-2488
1089-7658
DOI:10.1063/1.3534010