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Highly Accurate Analytical Approximate Solution to a Nonlinear Pseudo-Oscillator.
- Source :
-
Zeitschrift für Naturforschung Section A: A Journal of Physical Sciences . Jul2017, Vol. 72 Issue 7, p673-676. 4p. - Publication Year :
- 2017
-
Abstract
- A second-order Newton method is presented to construct analytical approximate solutions to a nonlinear pseudo-oscillator in which the restoring force is inversely proportional to the dependent variable. The nonlinear equation is first expressed in a specific form, and it is then solved in two steps, a predictor and a corrector step. In each step, the harmonic balance method is used in an appropriate manner to obtain a set of linear algebraic equations. With only one simple second-order Newton iteration step, a short, explicit, and highly accurate analytical approximate solution can be derived. The approximate solutions are valid for all amplitudes of the pseudo-oscillator. Furthermore, the method incorporates second-order Taylor expansion in a natural way, and it is of significant faster convergence rate. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 09320784
- Volume :
- 72
- Issue :
- 7
- Database :
- Academic Search Index
- Journal :
- Zeitschrift für Naturforschung Section A: A Journal of Physical Sciences
- Publication Type :
- Academic Journal
- Accession number :
- 123990581
- Full Text :
- https://doi.org/10.1515/zna-2017-0127