Geodesic
Applying the method of integration of ordinary differential equations based on the Chebyshev series to the restricted plane circular three-body problem
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2021), pp. 31-36

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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. An algorithm is briefly discussed to partition the integration interval into elementary subintervals where an approximate solution is represented by partial sums of shifted Chebyshev series with a prescribed accuracy. The efficiency of the proposed method is illustrated by solving the following problem of celestial mechanics: the plane circular restricted three-body problem. The reliability of the used error estimate and its proximity to the true error are shown. A number of advantages of the proposed method over the well-known Gear method of solving ordinary differential equations are analyzed. 
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     author = {O. B. Arushanyan and S. F. Zaletkin},
     title = {Applying the method of integration of ordinary differential equations based on the {Chebyshev} series to the restricted plane circular three-body problem},
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     pages = {31--36},
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O. B. Arushanyan; S. F. Zaletkin. Applying the method of integration of ordinary differential equations based on the Chebyshev series to the restricted plane circular three-body problem. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2021), pp. 31-36. http://geodesic.mathdoc.fr/item/VMUMM_2021_3_a3/