Geodesic
To the orthogonal expansion theory of the solution to the Cauchy problem for second-order ordinary differential equations
Numerical methods and programming, Tome 19 (2018) no. 2, pp. 178-184.

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A solvability theorem is proved for a nonlinear system of equations with respect to the approximate Chebyshev coefficients of the highest derivative in an ordinary differential equation. This theorem is a theoretical substantiation for the previously proposed approximate method of solving canonical systems of second-order ordinary differential equations using orthogonal expansions on the basis of Chebyshev polynomials of the first kind.
Keywords: ordinary differential equations, Cauchy problem, approximate analytical methods, numerical methods, orthogonal expansions, shifted Chebyshev series
Mots-clés : Markov's quadrature formulas. 
@article{VMP_2018_19_2_a5,
     author = {O. B. Arushanyan and S. F. Zaletkin},
     title = {To the orthogonal expansion theory of the solution to the {Cauchy} problem for second-order ordinary differential equations},
     journal = {Numerical methods and programming},
     pages = {178--184},
     publisher = {mathdoc},
     volume = {19},
     number = {2},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2018_19_2_a5/}
}
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O. B. Arushanyan; S. F. Zaletkin. To the orthogonal expansion theory of the solution to the Cauchy problem for second-order ordinary differential equations. Numerical methods and programming, Tome 19 (2018) no. 2, pp. 178-184. http://geodesic.mathdoc.fr/item/VMP_2018_19_2_a5/