Evaluation of integrated solution numerical method of mathematical model of mechanical oscillatory system dynamics
DOI:
https://doi.org/10.15587/2313-8416.2016.58823Keywords:
mathematical model, time domain, oscillatory system, numerical method, calculation errorAbstract
A comparative analysis of the accuracy solutions of linear differential equations in the time domain to the developed integrated and a number of famous classical numerical methods is done. Test model examples show the high efficiency of the proposed numerical method regarding problems of analysis of dynamic processes of mechanical oscillatory systems
References
Кrilov, V. I., Bobkov, V. V., Monastirniy, P. I. (1976). Vichislitelniye metodi. Vol. 1. Мoscow: Nаuка, 302.
Hairer, E., Nersett, С., Vanner, R. (1990). Resheniye obiknovennih differencialnih uravneniy. Nejestkiye zadachi. Мoscow: Мir, 512.
Basov, K. A. (2006). ANSYS и LMS Virtual Lab. Geometricheskoe modelirovaniye. Мoscow: DMK Press, 240.
Norenkov, I. P., Evstifeev, Y. А., Manichev, V. B. (1987). Adaptivniy metod uskorennogo analiza mnogoperiodnih elektronnih shеm. Izv. VUZov. Ser. Radioelectronika, 30 (6), 47–51.
Zhuk, D. М., Маnichev, V. B., Ilnickiy, А. О.; Stempkovskiy, А. L. (Ed.) (2008). Metodi i algoritmi resheniya differencialno-аlgebraicheskih uravneniy dlya modelirovaniya dinamiki tehnicheskih system i оbiektov. Problemi razrabotki perspektivnih mikro- i nanoelectronnih system. Мoscow: IPPМ RАN, 109–113.
Dyachenko, P. V. (2014). Kompiyterne modeliyvannya dinamiki kolivalynih procesiv mehanichnih system klasu zubchatih peredach. MONU. Cherkasskiy derjavniy tehnologichniy universitet. Cherkasy, 20.
Dyachenko, P. V. (2012) Prostorova matematichna model vlasnih chastot i form kolivany mechanichnoi systemi, klasy odnostupinchastih, evolventnih zubchastih peredach. Shtuchniy intelekt, 1, 54–60.
Maffezzoni, P., Codecasa, L., D’Amore, D. (2007). Time-Domain Simulation of Nonlinear Circuits Through Implicit Runge-Kutta Methods. IEEE Transactions on Circuits and Systems I: Regular Papers, 54 (2), 391–400. doi: 10.1109/tcsi.2006.887476
Butcher, J. C. (2008). Numerical methods for ordinary differential equations. John Wiley & Sons, 463. doi: 10.1002/9780470753767
Petzold, L. R., Jay, L. O., Yen, J. (1997). Numerical solution of highly oscillatory ordinary differential equations. Acta Numerica, 6, 437. doi: 10.1017/s0962492900002750
Downloads
Published
Issue
Section
License
Copyright (c) 2016 Петрo Васильович Дяченко
This work is licensed under a Creative Commons Attribution 4.0 International License.
Our journal abides by the Creative Commons CC BY copyright rights and permissions for open access journals.
Authors, who are published in this journal, agree to the following conditions:
1. The authors reserve the right to authorship of the work and pass the first publication right of this work to the journal under the terms of a Creative Commons CC BY, which allows others to freely distribute the published research with the obligatory reference to the authors of the original work and the first publication of the work in this journal.
2. The authors have the right to conclude separate supplement agreements that relate to non-exclusive work distribution in the form in which it has been published by the journal (for example, to upload the work to the online storage of the journal or publish it as part of a monograph), provided that the reference to the first publication of the work in this journal is included.
