Difference Scheme on a Uniform Grid for the Singularly Perturbed Cauchy Problem

We consider the Cauchy problem for a singularly perturbed second order ordinary differential equation. Based on the maximum principle, we estimate the solution and its derivatives. We construct an exponential fitted scheme generalizing the well-known scheme due to A. M. Il’in. We also prove the unif...

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2013-12, Vol.195 (6), p.865-872
Main Authors: Zadorin, A. I., Tikhovskaya, S. V.
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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Summary:We consider the Cauchy problem for a singularly perturbed second order ordinary differential equation. Based on the maximum principle, we estimate the solution and its derivatives. We construct an exponential fitted scheme generalizing the well-known scheme due to A. M. Il’in. We also prove the uniform convergence with the first order accuracy and illustrate the results by numerical experiments. Bibliography: 8 titles.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-013-1625-x