Geodesic
Accuracy of symmetric multi-step methods for the numerical modelling of satellite motion
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 13 (2020) no. 6, pp. 781-791.

Voir la notice de l'article provenant de la source Math-Net.Ru

Stability of high-order linear multistep Störmer–Cowell and symmetric methods are discussed in detail in this paper. Efficient algorithms for obtaining intervals of absolute stability and periodicity are given for these methods. To demonstrate the accuracy of numerical integration of the orbit over an interval about one year two model problems are considered. First problem is the 3D Kepler problem. Second one is a specially designed 3D model problem that has the exact solution and simulates the Earth-Moon-satellite system.
Keywords: linear multistep method, symmetric method, Störmer–Cowell method, PECE scheme
Mots-clés : orbit. 
@article{JSFU_2020_13_6_a11,
     author = {Evgenia D. Karepova and Iliya R. Adaev and Yury V. Shan'ko},
     title = {Accuracy of symmetric multi-step methods for the numerical modelling of satellite motion},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {781--791},
     publisher = {mathdoc},
     volume = {13},
     number = {6},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2020_13_6_a11/}
}
TY  - JOUR
AU  - Evgenia D. Karepova
AU  - Iliya R. Adaev
AU  - Yury V. Shan'ko
TI  - Accuracy of symmetric multi-step methods for the numerical modelling of satellite motion
JO  - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
PY  - 2020
SP  - 781
EP  - 791
VL  - 13
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JSFU_2020_13_6_a11/
LA  - en
ID  - JSFU_2020_13_6_a11
ER  - 
%0 Journal Article
%A Evgenia D. Karepova
%A Iliya R. Adaev
%A Yury V. Shan'ko
%T Accuracy of symmetric multi-step methods for the numerical modelling of satellite motion
%J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
%D 2020
%P 781-791
%V 13
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JSFU_2020_13_6_a11/
%G en
%F JSFU_2020_13_6_a11
Evgenia D. Karepova; Iliya R. Adaev; Yury V. Shan'ko. Accuracy of symmetric multi-step methods for the numerical modelling of satellite motion. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 13 (2020) no. 6, pp. 781-791. http://geodesic.mathdoc.fr/item/JSFU_2020_13_6_a11/

[1] IGS ftp archives, (Last accessed 4 Aug. 2020) ftp://ftp.igs.org/pub/center/analysis/

[2] E. Everhart, “Implicit Single-Sequence Methods for Integrating Orbits”, Celestial Mechanics, 10 (1974), 35–55 | DOI | MR | Zbl

[3] G. Beutler, Numerische Integration gewöhnlicher Differentialgleichungssysteme: Prinzipien und Algorithmen, Mitt. Satell., Beobachtungsstn. Zimmerwald, No 23, 1990

[4] G. Beutler, Methods of Celestial Mechanics I: Physical, Mathematical, and Numerical Principles, Springer-Verlag, Berlin, 2005 | MR | Zbl

[5] G. Quinlan, S. Tremaine, “Symmetric multistep methods for the numerical integration of planetary orbits”, Astron. J., 100:5 (1990), 1694–1700 | DOI

[6] P. Henrici, Discrete Variable Methods in Ordinary Differential Equations, John Wiley and Sons, New York, 1969 | MR

[7] J.D. Lambert, Computational Methods in Ordinary Differential Equations, John Wiley and Sons, New York, 1973 | MR | Zbl

[8] T. Bordovitcina, The modern numerical methods in problems of celestial mechanics, Nauka, M., 1984 (in Russian) | MR

[9] E. Yairer, S. Norsett, G. Wanner, Solving Ordinary Differential Equations, Springer-Verlag, Berlin, 1987 | MR

[10] E. Vergbitckii, Basis of Numerical Methods, Vysshaya shkola, M., 2004 (in Russian)

[11] V. Avdushev, Numerical modeling of orbits, Izdat. NTI, Tomsk, 2010 (in Russian)

[12] J.C. Butcher, Numerical methods for ordinary differential equations, John Wiley and Sons, New York, 2016 | MR | Zbl

[13] S.Nørsett, A. Asheim, “Regarding the absolute stability of Störmer-Cowell methods”, Discrete and Continuous Dynamical Systems, 34:3 (2014), 1131–1146 | DOI | MR

[14] J.D. Lambert, “Symmetric Multistep Methods for Periodic Initial Value Problems”, J. Inst. Maths Applics, 18 (1976), 189–202 | DOI | MR | Zbl

[15] P. Chakravarti, P. Worland, “A class of self-starting methods for the numerical solution of $y'' = f (x, y)$”, BIT Numerical Mathematics, 11:4 (1971), 368–383 | DOI | MR | Zbl

[16] A. Hurwitz, “On the conditions under which an equation has only roots with negative real parts”, English translation by H. G. Bergmann, Selected Papers on Mathematical Trends in Control Theory, eds. R. Bellman, R. Kalaba Eds., Dover, New York, 1964, 70–82 | MR

[17] E. Jury, J. Blanchard, “A stability test for linear discrete systems in table form”, I.R.E. Proc., 49 (1961), 1947–1948

[18] E. Jury, “A modified stability table for linear discrete systems”, Proc. IEEE, 53 (1965), 184–185 | DOI

[19] E. Jury, Inners and the Stability of Linear Systems, John Wiley and Sons, New York, 1982 | MR