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Parametrically defined nonlinear differential equations, differential-algebraic equations, and implicit ODEs: Transformations, general solutions, and integration methodsстатья
Статья опубликована в высокорейтинговом журнале
Информация о цитировании статьи получена из
Web of Science,
Scopus
Статья опубликована в журнале из списка Web of Science и/или Scopus
Дата последнего поиска статьи во внешних источниках: 26 марта 2018 г.
- Авторы: Polyanin A.D., Zhurov A.I.
- Журнал: Applied Mathematics Letters
- Том: 64
- Год издания: 2017
- Издательство: Pergamon Press Ltd.
- Местоположение издательства: United Kingdom
- Первая страница: 59
- Последняя страница: 66
- DOI: 10.1016/j.aml.2016.08.006
- Аннотация: The study deals with nonlinear ordinary differential equations defined parametrically by two relations; these arise in fluid dynamics and are a special class of coupled differential-algebraic equations. We propose a few techniques for reducing such equations, first or second order, to systems of standard ordinary differential equations as well as techniques for the exact integration of these systems. Several examples show how to construct general solutions to some classes of nonlinear equations involving arbitrary functions. We specify a procedure for the numerical solution of the Cauchy problem for parametrically defined differential equations and related differential-algebraic equations. The proposed techniques are also effective for the numerical integration of problems for implicitly defined equations.
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