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Solving a second-order nonlinear singular perturbation ordinary differential equation by a Samarskii scheme

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Abstract

A boundary value problem for a second-order nonlinear singular perturbation ordinary differential equation is considered. A method based on Newton and Picard linearizations using a modified Samarskii scheme on a Shishkin grid for a linear problem is proposed. It is proved that the difference schemes are of second-order and uniformly convergent. To decrease the number of arithmetic operations, a two-grid method is proposed. The results of some numerical experiments are discussed.

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Authors and Affiliations

  1. Omsk Branch of Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, ul. Pevtsova 13, Omsk, 644099, Russia

    A. I. Zadorin & S. V. Tikhovskaya

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  1. A. I. Zadorin
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  2. S. V. Tikhovskaya
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Correspondence to A. I. Zadorin.

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Original Russian Text © A.I. Zadorin, S.V. Tikhovskaya, 2013, published in Sibirskii Zhurnal Vychislitel’noi Matematiki, 2013, Vol. 16, No. 1, pp. 11–25.

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Zadorin, A.I., Tikhovskaya, S.V. Solving a second-order nonlinear singular perturbation ordinary differential equation by a Samarskii scheme. Numer. Analys. Appl. 6, 9–23 (2013). https://doi.org/10.1134/S1995423913010023

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  • DOI: https://doi.org/10.1134/S1995423913010023

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