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

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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. 
@article{VNGU_2011_11_3_a7,
     author = {A. I. Zadorin and S. V. Tihovskaya},
     title = {Difference scheme on an uniform mesh  for a singularly perturbed {Cauchy} problem},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
     pages = {114--122},
     publisher = {mathdoc},
     volume = {11},
     number = {3},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VNGU_2011_11_3_a7/}
}
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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/