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Sibirskii Zhurnal Industrial'noi Matematiki, 2013, Volume 16, Number 1, Pages 42–55
(Mi sjim765)
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This article is cited in 5 scientific papers (total in 5 papers)
A two-grid method for a nonlinear singular perturbation boundary value problem on the Shishkin scheme
A. I. Zadorin, S. V. Tikhovskaya Omsk Deaprtment of the Sobolev Institute of Mathematics of the SDRAS, Omsk, Russia
Abstract:
Unders consideration is some boundary value problem for a second order nonlinear singular perturbation ordinary differential equationd. An upwind scheme on the Shishkin mesh is applied. We use the Newton and Picard methods to resolve the difference schemeare investigated. To decrease number of arithmetical operations we use the two-grid method. Application of the Richardson extrapolation is shown to give almost second order accuracy of the difference scheme. The results of some numerical experiments are discussed.
Keywords:
nonlinear differential equation, singular perturbation, Shishkin mesh, difference scheme, iterative method, two-grid method, Richardson extrapolation.
Received: 01.02.2013
Citation:
A. I. Zadorin, S. V. Tikhovskaya, “A two-grid method for a nonlinear singular perturbation boundary value problem on the Shishkin scheme”, Sib. Zh. Ind. Mat., 16:1 (2013), 42–55
Linking options:
https://www.mathnet.ru/eng/sjim765 https://www.mathnet.ru/eng/sjim/v16/i1/p42
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Abstract page: | 551 | Full-text PDF : | 154 | References: | 67 | First page: | 8 |
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