Journal of Mathematical Sciences

, Volume 195, Issue 6, pp 865–872 | Cite as

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 uniform convergence with the first order accuracy and illustrate the results by numerical experiments. Bibliography: 8 titles.


Boundary Layer Cauchy Problem Maximum Principle Uniform Convergence Uniform Grid 


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© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Omsk Branch of Sobolev Institute of Mathematics 13OmskRussia

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