Parametrically defined nonlinear differential equations, differential-algebraic equations, and implicit ODEs: transformations, general solutions, and integration methods

Polyanin, Andrei D. and Zhurov, Alexei ORCID: https://orcid.org/0000-0002-5594-0740 2017. Parametrically defined nonlinear differential equations, differential-algebraic equations, and implicit ODEs: transformations, general solutions, and integration methods. Applied Mathematics Letters 64 , pp. 59-66. 10.1016/j.aml.2016.08.006

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Abstract

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.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Dentistry Medicine
Uncontrolled Keywords:	Parametrically defined differential equations, Differential–algebraic equations, Nonlinear differential equations, Exact and numerical methods, Cauchy problem, Exact and general solutions
Publisher:	Elsevier
ISSN:	0893-9659
Date of Acceptance:	12 August 2016
Last Modified:	22 Oct 2022 13:27
URI:	https://orca.cardiff.ac.uk/id/eprint/103699

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