Geodesic
An error estimate for an approximate solution to ordinary differential equations obtained using the Chebyshev series
Numerical methods and programming, Tome 21 (2020) no. 3, pp. 241-250.

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An approximate method of solving the Cauchy problem for nonlinear first-order ordinary differential equations is considered. The method is based on using the shifted Chebyshev series and a Markov quadrature formula. Some approaches are given to estimate the error of an approximate solution expressed by a partial sum of a certain order series. The error is estimated using the second approximation of the solution expressed by a partial sum of a higher order series. An algorithm of partitioning the integration interval into elementary subintervals to ensure the computation of the solution with a prescribed accuracy is discussed on the basis of the proposed approaches to error estimation.
Keywords: ordinary differential equations; approximate analytical methods; numerical methods; orthogonal expansions; shifted Chebyshev series; Markov quadrature formulas; polynomial approximation; precision control; error estimate; automatic step size control. 
@article{VMP_2020_21_3_a3,
     author = {O. B. Arushanyan and S. F. Zaletkin},
     title = {An error estimate for an approximate solution to ordinary differential equations obtained using the {Chebyshev} series},
     journal = {Numerical methods and programming},
     pages = {241--250},
     publisher = {mathdoc},
     volume = {21},
     number = {3},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2020_21_3_a3/}
}
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O. B. Arushanyan; S. F. Zaletkin. An error estimate for an approximate solution to ordinary differential equations obtained using the Chebyshev series. Numerical methods and programming, Tome 21 (2020) no. 3, pp. 241-250. http://geodesic.mathdoc.fr/item/VMP_2020_21_3_a3/