Geodesic
Numerical method for a system of linear equations of second order with a small parameter on a semi-infinite interval
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 7 (2004) no. 2, pp. 103-114 
A. I. Zadorin; O. V. Kharina. Numerical method for a system of linear equations of second order with a small parameter on a semi-infinite interval. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 7 (2004) no. 2, pp. 103-114. http://geodesic.mathdoc.fr/item/SJVM_2004_7_2_a1/
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     title = {Numerical method for a~system of linear equations of second order with a~small parameter on a~semi-infinite interval},
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Voir la notice de l'article provenant de la source Math-Net.Ru

A boundary value problem for a linear system of ordinary second order differential equations with a small parameter at higher derivatives on a semi-infinite interval is considered. Systems of reaction-diffusion and convection-diffusion equations are considered. The method of reduction of a problem to a finite interval problem, based on the extraction of a set of solutions satisfying the limit conditions on infinity, is investigated. Auxiliary singular Cauchy problems for the differential matrix Riccati equations are solved with the use of a series in powers of a small parameter and an independent variable. Accuracy of the method proposed is estimated. The Shishkin mesh is proposed for solving a problem after its reduction to a finite interval. The results of numerical experiments are presented.

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