Geodesic
The transfer of the boundary condition from the infinity for the numerical solution to the second order equations with a small parameter
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 2 (1999) no. 1, pp. 21-35 
A. I. Zadorin. The transfer of the boundary condition from the infinity for the numerical solution to the second order equations with a small parameter. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 2 (1999) no. 1, pp. 21-35. http://geodesic.mathdoc.fr/item/SJVM_1999_2_1_a2/
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Voir la notice de l'article provenant de la source Math-Net.Ru

The ordinary second order differential equations with a small parameter effecting the higher derivative on the semi-infinite interval are considered. The method of the transition of that problem to the finite interval is proposed. To solve the auxiliary Cauchy problem the asymptotic method is used.

[1] Abramov A. A., Balla K., Konyukhova N. B., Perenos granichnykh uslovii iz osobykh tochek dlya sistem obyknovennykh differentsialnykh uravnenii, Soobsch. po vychisl. matem., VTs AN SSSR, M., 1981 | MR

[2] Konyukhova N. B., Gladkie mnogoobraziya Lyapunova i singulyarnye kraevye zadachi, Soobsch. po vychisl. matem., VTs AN SSSR, M., 1996

[3] Birger E. S., Lyalikova N. B., “O nakhozhdenii dlya nekotorykh sistem obyknovennykh differentsialnykh uravnenii reshenii s zadannym usloviem na beskonechnosti”, Zhurn. vychisl. matem. i mat. fiz., 5:6 (1965), 979–990 | MR | Zbl

[4] Klokov Yu. A., Kraevye zadachi s usloviem na beskonechnosti dlya uravnenii matematicheskoi fiziki, Rizhskii institut inzhenerov grazhdanskogo vozdushnogo flota, Riga, 1963

[5] Bakhvalov N. S., Zhidkov N. P., Kobelkov G. M., Chislennye metody, Nauka, M., 1987 | MR | Zbl

[6] Dulan E., Miller D., Shilders U., Ravnomernye chislennye metody resheniya zadach s pogranichnym sloem, Mir, M., 1983 | MR

[7] Zadorin A. I., “Raznostnaya skhema dlya samosopryazhennoi singulyarno vozmuschennoi tretei kraevoi zadachi”, Modelirovanie v mekhanike — Novosibirsk, 3:1 (1989), 77–82 | MR | Zbl

[8] Bakhvalov N. S., “K optimizatsii metodov resheniya kraevykh zadach pri nalichii pogranichnogo sloya”, Zhurn. vychisl. matem. i mat. fiz., 9:4 (1969), 841–890

[9] Boglaev I. P., “O chislennom integrirovanii singulyarno-vozmuschennoi zadachi Koshi dlya obyknovennogo differentsialnogo uravneniya”, Zhurn. vychisl. matem. i mat. fiz., 25:7 (1985), 1009–1022 | MR | Zbl

[10] Zeldovich Ya. B., Barenblatt G. I., Librovich V. B. i dr., Matematicheskaya teoriya goreniya i vzryva, Nauka, M., 1980 | MR