Geodesic
Simultaneous approximation of the solution and its derivatives in a boundary value problem for a linear differential equation with polynomial coefficients
Izvestiya. Mathematics , Tome 38 (1992) no. 3, pp. 553-573.

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

The author investigates an algorithm for the construction of a polynomial that realizes the simultaneous approximation of the solution of a boundary value problem and its derivatives with the same rapidity of decrease of the error as for the case of the best uniform polynomial approximation of the function on an interval. 
@article{IM2_1992_38_3_a5,
     author = {E. S. Sinaiskii},
     title = {Simultaneous approximation of the solution and its derivatives in a boundary value problem for a linear differential equation with polynomial coefficients},
     journal = {Izvestiya. Mathematics },
     pages = {553--573},
     publisher = {mathdoc},
     volume = {38},
     number = {3},
     year = {1992},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1992_38_3_a5/}
}
TY  - JOUR
AU  - E. S. Sinaiskii
TI  - Simultaneous approximation of the solution and its derivatives in a boundary value problem for a linear differential equation with polynomial coefficients
JO  - Izvestiya. Mathematics 
PY  - 1992
SP  - 553
EP  - 573
VL  - 38
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1992_38_3_a5/
LA  - en
ID  - IM2_1992_38_3_a5
ER  - 
%0 Journal Article
%A E. S. Sinaiskii
%T Simultaneous approximation of the solution and its derivatives in a boundary value problem for a linear differential equation with polynomial coefficients
%J Izvestiya. Mathematics 
%D 1992
%P 553-573
%V 38
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1992_38_3_a5/
%G en
%F IM2_1992_38_3_a5
E. S. Sinaiskii. Simultaneous approximation of the solution and its derivatives in a boundary value problem for a linear differential equation with polynomial coefficients. Izvestiya. Mathematics , Tome 38 (1992) no. 3, pp. 553-573. http://geodesic.mathdoc.fr/item/IM2_1992_38_3_a5/

[1] Dzyadyk V. K., “Approksimatsionnyi metod priblizheniya algebraicheskimi mnogochlenami reshenii lineinykh differentsialnykh uravnenii”, Izv. AN SSSR. Ser. matem., 38:4 (1974), 937–967 | MR | Zbl

[2] Dzyadyk V. K., Approksimatsionnye metody resheniya differentsialnykh i integralnykh uravnenii, Nauk. dumka, Kiev, 1988, s. 304 | MR

[3] Ostrovetskii L. A., “Reshenie po $\operatorname{A}$-metodu mnogotochechnykh kraevykh zadach”, Nekotorye voprosy teorii approksimatsii funktsii, In-t matematiki AN USSR, Kiev, 1985, 94–100 | MR

[4] Sinaiskii E. S., “Approksimatsionnyi metod v odnoi kraevoi zadache dlya lineinogo differentsialnogo uravneniya s mnogochlennymi koeffitsientami”, Ukr. matem. zhurn., 40:2 (1988), 248–253 | MR

[5] Lomakin V. A., Teoriya uprugosti neodnorodnykh tel, Izd-vo MGU, M., 1976, s. 368

[6] Gelfond A. O., “O mnogochlenakh, naimenee uklonyayuschikhsya ot nulya vmeste so svoimi proizvodnymi”, DAN SSSR, 96:4 (1954), 689–691 | MR

[7] Goncharov V. L., Teoriya interpolirovaniya i priblizheniya funktsii, Gostekhteorizdat, M., 1954, s. 328

[8] Zabreiko P. P., Koshelev A. I., Krasnoselskii M. A. i dr., Integralnye uravneniya, Nauka, M., 1968, s. 448

[9] Bekkenbakh E., Bellman R., Neravenstva, Mir, M., 1965, s. 276 | MR

[10] Suetin P. K., Klassicheskie ortogonalnye mnogochleny, Nauka, M., 1976, s. 328 | MR

[11] Bakhvalov N. S., Chislennye metody, Nauka, M., 1973, s. 632 | MR | Zbl

[12] Polia G., Sege G., Zadachi i teoremy iz analiza. V 2-kh ch., Ch. 2. Teoriya funktsii. Raspredelenie nulei. Polinomy. Opredeliteli. Teoriya chisel, Nauka, M., 1978, s. 432

[13] Lantsosh K., Prakticheskie metody prikladnogo analiza, Fizmatgiz, M., 1961, s. 524