Geodesic
Solvability of a system of equations for the Fourier-Chebyshev coefficients when solving ordinary differential equations by the Chebyshev series method
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (2017), pp. 58-61

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A solvability theorem for a system of equations with respect to approximate values of Fourier–Chebyshev coefficients is formulated. This theorem is a theoretical substantiation for the numerical solution of ordinary differential equations using Chebyshev series. 
@article{VMUMM_2017_5_a10,
     author = {O. B. Arushanyan and S. F. Zaletkin},
     title = {Solvability of a system of equations for the {Fourier-Chebyshev} coefficients when solving ordinary differential equations by the {Chebyshev} series method},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {58--61},
     publisher = {mathdoc},
     number = {5},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2017_5_a10/}
}
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O. B. Arushanyan; S. F. Zaletkin. Solvability of a system of equations for the Fourier-Chebyshev coefficients when solving ordinary differential equations by the Chebyshev series method. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (2017), pp. 58-61. http://geodesic.mathdoc.fr/item/VMUMM_2017_5_a10/