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

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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/}
}
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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/