Mathematical modeling of close encounters of Solar system small bodies with major planets and the Moon
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 2 (2007), pp. 151-154.

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We establish the choice of numerical integration method for the motion equations of solar system small bodies in moments of close encounters with major planets and the Moon. The performed research shows that the multi-step Adams–Moulton method with preliminary chosen smaller step and increased order of approximation is more preferable for these moments. The modeling of moments of encounters using the one-step Everhart method with variable step sufficiently increases the global time of numerical process and requires the following optimization of step change criterion.
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V. V. Abramov. Mathematical modeling of close encounters of Solar system small bodies with major planets and the Moon. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 2 (2007), pp. 151-154. http://geodesic.mathdoc.fr/item/VSGTU_2007_2_a37/

[1] Dzh. Kholl., Dzh. Uatt, Sovremennye chislennye metody resheniya obyknovennykh differentsialnykh uravnenii, Mir, M., 1979

[2] Abramov V. V., “Primenenie metodov Adamsa k resheniyu uravnenii dvizheniya bolshikh planet, Luny i Solntsa”, Tr. Tretei Vseros. nauchn. konf. Ch. 3, Mat. modelirovanie i kraevye zadachi, SamGTU, Samara, 2006, 13–19

[3] Abramov V. V., “Effektivnost metoda Adamsa–Multona pri matematicheskom modelirovanii dvizheniya malykh tel Solnechnoi sistemy”, Nelineinyi dinamicheskii analiz-2007, Tez. dokl. mezhdunar. kongr., SPbGU, SPb., 2007

[4] Everhart E., “Implicit single methods for integrating orbits”, Celestial Mechanics, 1974, no. 10, 35–55 | DOI | MR | Zbl

[5] A. F. Zausaev, A. A. Zausaev, A. G. Olkhin, “Primenenie metoda Everkharta 31-go poryadka dlya resheniya uravnenii dvizheniya bolshikh planet”, Tr. GAISh, 75, 2004, 209–210, VAK-2004

[6] X. X. Newhall, E. M. Standish Jr., J. G. Williams, “DE102: a numerically integrated ephemeris of the Moon and planets spanning forty-four centuries”, Astron. Astrophys., 1983, no. 125, 150–167 | Zbl

[7] V. V. Abramov, S. S. Denisov, L. A. Solovev, “Modelirovanie sblizhenii asteroida 99942 Apophis s vnutrennimi planetami i Lunoi”, Tez. dokl. XXXII Samarskoi obl. stud. nauchn. konf., Ch. 1, Samara, 2006, 101

[8] Abramov V. V., “Matematicheskoe modelirovanie dvizheniya malykh tel Solnechnoi sistemy na osnove metodov Adamsa”, Vestn. Sam. gos. tekhn. un-ta. Ser.: Fiz.-mat. nauki, 2006, no. 43, 192–194 | DOI