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Zh. Vychisl. Mat. Mat. Fiz., 2007, Volume 47, Number 7, Pages 1158–1178 (Mi zvmmf276)  

Singular problem for a third-order nonlinear ordinary differential equation arising in fluid dynamics

A. L. Duischkoa, N. B. Konyukhovaa, A. I. Sukovb

a Dorodnicyn Computing Centre, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119991, Russia
b Moscow State Technological University "Stankin", Vadkovskii per. 3a, Moscow, 101472, Russia

Abstract: Results concerning singular Cauchy problems, smooth manifolds, and Lyapunov series are used to correctly state and analyze a singular “initial-boundary” problem for a third-order nonlinear ordinary differential equation defined on the entire real axis. This problem arises in viscous incompressible fluid dynamics and describes self-similar solutions to the boundary layer equation for the stream function with a zero pressure gradient (plane-parallel flow in a mixing layer). The analysis of the problem suggests a simple numerical method for its solution. Numerical results are presented.

Key words: boundary layer equations, self-similar solution, third-order autonomous nonlinear ODE, singular problem on the entire real line, regular and singular solutions.

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English version:
Computational Mathematics and Mathematical Physics, 2007, 47:7, 1108–1128

Bibliographic databases:

UDC: 519.624.3
Received: 12.05.2005
Revised: 01.11.2006

Citation: A. L. Duischko, N. B. Konyukhova, A. I. Sukov, “Singular problem for a third-order nonlinear ordinary differential equation arising in fluid dynamics”, Zh. Vychisl. Mat. Mat. Fiz., 47:7 (2007), 1158–1178; Comput. Math. Math. Phys., 47:7 (2007), 1108–1128

Citation in format AMSBIB
\Bibitem{DuiKonSuk07}
\by A.~L.~Duischko, N.~B.~Konyukhova, A.~I.~Sukov
\paper Singular problem for a~third-order nonlinear ordinary differential equation arising in fluid dynamics
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2007
\vol 47
\issue 7
\pages 1158--1178
\mathnet{http://mi.mathnet.ru/zvmmf276}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2376658}
\transl
\jour Comput. Math. Math. Phys.
\yr 2007
\vol 47
\issue 7
\pages 1108--1128
\crossref{https://doi.org/10.1134/S0965542507070044}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-34547672942}


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  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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