Geodesic
Justification of some approach to implementation of orthogonal expansions for approximate integration of canonical systems of second order
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2018), pp. 29-33

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A solvability theorem for a nonlinear system of equations with respect to approximate values of Fourier–Chebyshev coefficients is proved. This theorem is a theoretical substantiation for the numerical solution of second order ordinary differential equations using Chebyshev series and Markov quadrature formulas. 
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     author = {O. B. Arushanyan and S. F. Zaletkin},
     title = {Justification of some approach to implementation of orthogonal expansions for approximate integration of canonical systems of second order},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {29--33},
     publisher = {mathdoc},
     number = {3},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2018_3_a4/}
}
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O. B. Arushanyan; S. F. Zaletkin. Justification of some approach to implementation of orthogonal expansions for approximate integration of canonical systems of second order. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2018), pp. 29-33. http://geodesic.mathdoc.fr/item/VMUMM_2018_3_a4/