Geodesic
Analysis of a~difference scheme for a~singular perturbation Cauchy problem on refined grids
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 14 (2011) no. 1, pp. 47-57

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A Cauchy problem for a singular perturbation second-order ordinary differential equation is considered. It is proved that the upwind difference scheme on a grid proposed by Shishkin is uniformly convergent. The grid is well known only in application to a boundary value problem. The results of some numerical experiments are discussed. 
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     author = {A. I. Zadorin and S. V. Tikhovskaya},
     title = {Analysis of a~difference scheme for a~singular perturbation {Cauchy} problem on refined grids},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
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A. I. Zadorin; S. V. Tikhovskaya. Analysis of a~difference scheme for a~singular perturbation Cauchy problem on refined grids. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 14 (2011) no. 1, pp. 47-57. http://geodesic.mathdoc.fr/item/SJVM_2011_14_1_a4/