Geodesic
On solvability of a nonlinear system of equations for the Fourier-Chebyshev coefficients in the problem of solving ordinary differential equations using Chebyshev series
Numerical methods and programming, Tome 18 (2017) no. 2, pp. 169-174.

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

A solvability theorem for a nonlinear system of equations with respect to approximate values of Fourier-Chebyshev coefficients is formulated and proved. This theorem is a theoretical substantiation for the previously proposed numerical-analytical method of solving ordinary differential equations using Chebyshev series.
Keywords: ordinary differential equations, approximate analytical methods, numerical methods, orthogonal expansions, shifted Chebyshev series
Mots-clés : Markov's quadrature formulas. 
@article{VMP_2017_18_2_a6,
     author = {O. B. Arushanyan and S. F. Zaletkin},
     title = {On solvability of a nonlinear system of equations for the {Fourier-Chebyshev} coefficients in the problem of solving ordinary differential equations using {Chebyshev} series},
     journal = {Numerical methods and programming},
     pages = {169--174},
     publisher = {mathdoc},
     volume = {18},
     number = {2},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2017_18_2_a6/}
}
TY  - JOUR
AU  - O. B. Arushanyan
AU  - S. F. Zaletkin
TI  - On solvability of a nonlinear system of equations for the Fourier-Chebyshev coefficients in the problem of solving ordinary differential equations using Chebyshev series
JO  - Numerical methods and programming
PY  - 2017
SP  - 169
EP  - 174
VL  - 18
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VMP_2017_18_2_a6/
LA  - ru
ID  - VMP_2017_18_2_a6
ER  - 
%0 Journal Article
%A O. B. Arushanyan
%A S. F. Zaletkin
%T On solvability of a nonlinear system of equations for the Fourier-Chebyshev coefficients in the problem of solving ordinary differential equations using Chebyshev series
%J Numerical methods and programming
%D 2017
%P 169-174
%V 18
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VMP_2017_18_2_a6/
%G ru
%F VMP_2017_18_2_a6
O. B. Arushanyan; S. F. Zaletkin. On solvability of a nonlinear system of equations for the Fourier-Chebyshev coefficients in the problem of solving ordinary differential equations using Chebyshev series. Numerical methods and programming, Tome 18 (2017) no. 2, pp. 169-174. http://geodesic.mathdoc.fr/item/VMP_2017_18_2_a6/