Geodesic
A numerical method for a~system of equations with a~small parameter and a~point source on an infinite interval
Sibirskij žurnal industrialʹnoj matematiki, Tome 8 (2005) no. 4, pp. 149-157.

Voir la notice de l'article provenant de la source Math-Net.Ru

A method for solving a boundary-value problem on an infinite interval is considered for a linear system of second-order ordinary differential equations with a small parameter at the highest derivatives and a point source. The question is addressed of reduction of this problem to a finite interval. A mesh, condensing in the boundary layer, is used for numerical solution of a system of singularly perturbed equations on a finite interval. 
@article{SJIM_2005_8_4_a11,
     author = {O. V. Kharina},
     title = {A numerical method for a~system of equations with a~small parameter and a~point source on an infinite interval},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {149--157},
     publisher = {mathdoc},
     volume = {8},
     number = {4},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2005_8_4_a11/}
}
TY  - JOUR
AU  - O. V. Kharina
TI  - A numerical method for a~system of equations with a~small parameter and a~point source on an infinite interval
JO  - Sibirskij žurnal industrialʹnoj matematiki
PY  - 2005
SP  - 149
EP  - 157
VL  - 8
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SJIM_2005_8_4_a11/
LA  - ru
ID  - SJIM_2005_8_4_a11
ER  - 
%0 Journal Article
%A O. V. Kharina
%T A numerical method for a~system of equations with a~small parameter and a~point source on an infinite interval
%J Sibirskij žurnal industrialʹnoj matematiki
%D 2005
%P 149-157
%V 8
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SJIM_2005_8_4_a11/
%G ru
%F SJIM_2005_8_4_a11
O. V. Kharina. A numerical method for a~system of equations with a~small parameter and a~point source on an infinite interval. Sibirskij žurnal industrialʹnoj matematiki, Tome 8 (2005) no. 4, pp. 149-157. http://geodesic.mathdoc.fr/item/SJIM_2005_8_4_a11/

[1] Voevodin V. V., Kuznetsov Yu. A., Matritsy i vychisleniya, Nauka, M., 1984 | MR | Zbl

[2] Abramov A. A., “O perenose usloviya ogranichennosti dlya nekotorykh sistem obyknovennykh lineinykh differentsialnykh uravnenii”, Zhurn. vychisl. matematiki i mat. fiziki, 1:4 (1961), 733–737 | MR | Zbl

[3] Miller J. J. H., O'Riordan E., Shishkin G. I., Fitted Numerical Methods for Singular Perturbation Problems. Error Estimates in the Maximum Norm for Linear Problems in One and Two Dimensions, World Scientific, Singapore, 1996 | MR

[4] Abramov A. A., Balla K., Konyukhova N. B., Perenos granichnykh uslovii iz osobykh tochek dlya sistem lineinykh obyknovennykh differentsialnykh uravnenii, izd. VTs AN SSSR, M., 1981 | MR | Zbl

[5] Harina O. V., Zadorin A. I., “Numerical solution of a boundary value problem for a linear system of equations with a small parameter on a half-infinite interval”, Proc. Internat. Conf. Computational Mathematics, Part 2, Novosibirsk, 2002, 449–453 | MR

[6] Alefeld G., Schneider N., “On square roots of $M$-matrices”, Linear Algebra and its Applications, 1982, no. 42, 119–132 | DOI | MR | Zbl

[7] Ikramov Kh. D., Chislennoe reshenie matrichnykh uravnenii, Nauka, M., 1984 | MR | Zbl