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Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 2011, Volume 11, Issue 3, Pages 114–122 (Mi vngu92)  

Difference scheme on an uniform mesh for a singularly perturbed Cauchy problem

A. I. Zadorin, S. V. Tihovskaya

Omsk Branch of Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: Cauchy problem for a singularly perturbed second order ordinary differential equation is considered. On a base of introduced maximum principle for a Cauchy problem the solution and its derivateves are estimated. Exponential fitted scheme, generalized well-known Il'in scheme for a case of an initial value problem, is constructed. The uniform convergence of constructed scheme with the first order of an accuracy is proved. Numerical results are discussed.

Keywords: second order ordinary differential equation, singular perturbation, Cauchy problem, difference scheme, maximum principle, exponential fitted scheme, uniform convergence.

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English version:
Journal of Mathematical Sciences, 2013, 195:6, 865–872

UDC: 519.62
Received: 09.05.2010

Citation: A. I. Zadorin, S. V. Tihovskaya, “Difference scheme on an uniform mesh for a singularly perturbed Cauchy problem”, Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 11:3 (2011), 114–122; J. Math. Sci., 195:6 (2013), 865–872

Citation in format AMSBIB
\Bibitem{ZadTik11}
\by A.~I.~Zadorin, S.~V.~Tihovskaya
\paper Difference scheme on an uniform mesh for a singularly perturbed Cauchy problem
\jour Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform.
\yr 2011
\vol 11
\issue 3
\pages 114--122
\mathnet{http://mi.mathnet.ru/vngu92}
\transl
\jour J. Math. Sci.
\yr 2013
\vol 195
\issue 6
\pages 865--872
\crossref{https://doi.org/10.1007/s10958-013-1625-x}


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  • Вестник Новосибирского государственного университета. Серия: математика, механика, информатика
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