This article is cited in 1 scientific paper (total in 1 paper)
Analysis of a difference scheme for a singular perturbation Cauchy problem on refined grids
A. I. Zadorin, S. V. Tikhovskaya
Omsk Branch of Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Science, Omsk
A Cauchy problem for a singular perturbation second-order ordinary differential equation is considered. It is proved that the upwind difference scheme on a grid proposed by Shishkin is uniformly convergent. The grid is well known only in application to a boundary value problem. The results of some numerical experiments are discussed.
second order ordinary differential equation, singular perturbation, Cauchy problem, difference scheme, maximum principle, Shishkin mesh, uniform convergence.
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Numerical Analysis and Applications, 2011, 4:1, 36–45
A. I. Zadorin, S. V. Tikhovskaya, “Analysis of a difference scheme for a singular perturbation Cauchy problem on refined grids”, Sib. Zh. Vychisl. Mat., 14:1 (2011), 47–57; Num. Anal. Appl., 4:1 (2011), 36–45
Citation in format AMSBIB
\by A.~I.~Zadorin, S.~V.~Tikhovskaya
\paper Analysis of a~difference scheme for a~singular perturbation Cauchy problem on refined grids
\jour Sib. Zh. Vychisl. Mat.
\jour Num. Anal. Appl.
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Tikhovskaya S.V., “Analysis of the Numerical Differentiation Formulas of Functions With Large Gradients”, Application of Mathematics in Technical and Natural Sciences, AIP Conference Proceedings, 1895, ed. Todorov M., Amer Inst Physics, 2017, UNSP 110010-1
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