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

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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. 
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     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/}
}
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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/