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Zh. Vychisl. Mat. Mat. Fiz., 2009, Volume 49, Number 12, Pages 2131–2143 (Mi zvmmf4794)  

Steplike contrast structures for a second-order ordinary differential equation with a small parameter multiplying the highest derivative

S. F. Dolbeeva, E. A. Rozhdestvenskaya

Chelyabinsk State University, ul. Brat'ev Kashirinykh 129, Chelyabinsk, 454021, Russia

Abstract: A boundary value problem is considered for a second-order nonlinear ordinary differential equation with a small parameter multiplying the highest derivative. The limit equation has three solutions, of which two are stable and are separated by the third unstable one. For the original problem, an asymptotic expansion of a solution is studied that undergoes a jump from one stable root of the limit equation to the other in the neighborhood of a certain point. A uniform asymptotic approximation of this solution is constructed up to an arbitrary power of the small parameter.

Key words: asymptotic expansion, boundary value problem for a second-order ordinary differential equation with a small parameter.

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English version:
Computational Mathematics and Mathematical Physics, 2009, 49:12, 2034–2046

Bibliographic databases:

UDC: 519.624.2
Received: 24.04.2009

Citation: S. F. Dolbeeva, E. A. Rozhdestvenskaya, “Steplike contrast structures for a second-order ordinary differential equation with a small parameter multiplying the highest derivative”, Zh. Vychisl. Mat. Mat. Fiz., 49:12 (2009), 2131–2143; Comput. Math. Math. Phys., 49:12 (2009), 2034–2046

Citation in format AMSBIB
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\paper Steplike contrast structures for a~second-order ordinary differential equation with a~small parameter multiplying the highest derivative
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2009
\vol 49
\issue 12
\pages 2131--2143
\mathnet{http://mi.mathnet.ru/zvmmf4794}
\transl
\jour Comput. Math. Math. Phys.
\yr 2009
\vol 49
\issue 12
\pages 2034--2046
\crossref{https://doi.org/10.1134/S0965542509120045}
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  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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