Geodesic
A polynomial approximation method for the solution of a boundary value problem and its derivatives for linear ordinary differential equations
Izvestiya. Mathematics, Tome 33 (1989) no. 2, pp. 391-402 
V. K. Dzyadyk; L. A. Ostrovetskii. A polynomial approximation method for the solution of a boundary value problem and its derivatives for linear ordinary differential equations. Izvestiya. Mathematics, Tome 33 (1989) no. 2, pp. 391-402. http://geodesic.mathdoc.fr/item/IM2_1989_33_2_a8/
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Effective algorithms are proposed for the construction of polynomials of asymptotically best approximation of the solution of a boundary value problem and its derivatives for linear differential equations with polynomial coefficients. Bibliography: 7 titles.

[1] Krylov Ya. M., “Metody priblizhennogo resheniya zadach matematicheskoi fiziki”, Izbrannye trudy, 2, AN USSR, Kiev, 1961, 150–205

[2] Dzyadyk V. K., Ostrovetskii L. A., Priblizhenie mnogochlenami reshenii kraevykh zadach dlya obyknovennykh lineinykh differentsialnykh uravnenii, Preprint No 85.11, IM AN USSR, Kiev, 1985, 32 pp. | MR | Zbl

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

[4] Myuntts G., Integralnye uravneniya. Ch. 1. Lineinye uravneniya Volterra, Gostekhizdat, M., L, 1934, 330 pp.

[5] Dzyadyk V. K., “On a problem of Chebyshev and Markov”, Analysis Mathematica, 3:3 (1977), 171–175 | DOI | MR | Zbl

[6] Bernshtein S. N., “Ob odnom klasse ortogonalnykh mnogochlenov”, Sobr. soch., t. 1, AN SSSR, M., 1952, 452–465

[7] Akhiezer Ya. I., Lektsii po teorii approksimatsii, Nauka, M., 1965, 290–294 | MR