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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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},
     year = {2017},
     volume = {18},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2017_18_2_a6/}
}
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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/