دورية أكاديمية
Harmonic Balance for Non-Periodic Hyperbolic Solutions of Nonlinear Ordinary Differential Equations
| العنوان: | Harmonic Balance for Non-Periodic Hyperbolic Solutions of Nonlinear Ordinary Differential Equations |
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| المؤلفون: | Serge Bruno Yamgoue, Olivier Tiokeng Lekeufack, Timoleon Crepin Kofane |
| المصدر: | Mathematical Modelling and Analysis, Vol 22, Iss 2 (2017) |
| بيانات النشر: | Vilnius Gediminas Technical University, 2017. |
| سنة النشر: | 2017 |
| المجموعة: | LCC:Mathematics |
| مصطلحات موضوعية: | harmonic balance, linearization, explicit approximations, solitons, hyperbolic solutions, Mathematics, QA1-939 |
| الوصف: | In this paper, we propose a new approach for obtaining explicit analytical approximations to the homoclinic or heteroclinic solutions of a general class of strongly nonlinear ordinary differential equations describing conservative singledegree-of-freedom systems. Through a simple and explicit change of the independent variable that we introduce, these equations are transformed to others for which the original homoclinic or heteroclinic solutions are mapped into periodic solutions that satisfy some boundary conditions. Recent simplified methods of harmonic balance can then be exploited to construct highly accurate analytic approximations to these solutions. Here, we adopt the combination of Newton linearization with the harmonic balance to construct the approximates in incremental steps, thereby proposing both appropriate initial approximates and increments that together satisfy the required boundary conditions. Three examples including a septic Duffing oscillator, a controlled mechanical pendulum and a perturbed KdV equations are presented to illustrate the great accuracy and simplicity of the new approach. |
| نوع الوثيقة: | article |
| وصف الملف: | electronic resource |
| اللغة: | English |
| تدمد: | 13926292 1392-6292 1648-3510 |
| Relation: | https://journals.vgtu.lt/index.php/MMA/article/view/881; https://doaj.org/toc/1392-6292; https://doaj.org/toc/1648-3510 |
| DOI: | 10.3846/13926292.2017.1276983 |
| URL الوصول: | https://doaj.org/article/a890c1b84f214de6a1f70c658e5cf079 |
| رقم الأكسشن: | edsdoj.890c1b84f214de6a1f70c658e5cf079 |
| قاعدة البيانات: | Directory of Open Access Journals |
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Full Text Finder | تدمد: | 13926292 16483510 |
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| DOI: | 10.3846/13926292.2017.1276983 |