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

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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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     author = {A. I. Zadorin and O. V. Kharina},
     title = {Numerical method for a~system of linear equations of second order with a~small parameter on a~semi-infinite interval},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {103--114},
     publisher = {mathdoc},
     volume = {7},
     number = {2},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2004_7_2_a1/}
}
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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/