Geodesic
Difference scheme on an uniform mesh for a singularly perturbed Cauchy problem
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 11 (2011) no. 3, pp. 114-122 Cet article a éte moissonné depuis la source Math-Net.Ru

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Cauchy problem for a singularly perturbed second order ordinary differential equation is considered. On a base of introduced maximum principle for a Cauchy problem the solution and its derivateves are estimated. Exponential fitted scheme, generalized well-known Il'in scheme for a case of an initial value problem, is constructed. The uniform convergence of constructed scheme with the first order of an accuracy is proved. Numerical results are discussed.
Keywords: second order ordinary differential equation, Cauchy problem, difference scheme, maximum principle, exponential fitted scheme
Mots-clés : singular perturbation, uniform convergence. 
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A. I. Zadorin; S. V. Tihovskaya. Difference scheme on an uniform mesh for a singularly perturbed Cauchy problem. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 11 (2011) no. 3, pp. 114-122. http://geodesic.mathdoc.fr/item/VNGU_2011_11_3_a7/

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