Abstract
In this paper we compare several Runge-Kutta type methods of fourth-order when they are applied in the Equatorial Magnetic-Binary Problem (EMBP) for which the analytical solutions are not known. The results of the comparison are presented with tables and diagrams, and the most efficient method is proposed according to the used criteria which are described.
Similar content being viewed by others
References
Bettis, D. G.: 1978,Lecture Notes in Mathematics, Springer-Verlag, Vol. 631, pp. 166–170.
Dormand, J. R. and Prince, P. J.: 1980,J. Comput. Applied Math. 6, 19.
England, R.: 1969,Comput. J. 12, 166.
Enright, W. H., Hull, T. E., and Lindberg, D.: 1975, BIT,15, 10.
Fehlberg, E.: 1968, NASA Technical Report, No. 287.
Fehlberg, E.: 1969a,Computing 4, 93.
Fehlberg, E.: 1969b, NASA Technical Report, No. 315.
Fehlberg, E.: 1986,Computing 34, 265.
Fox, K.: 1984,Celes. Mech. 33, 127.
Gear, C. W.: 1969,Information Processing 68, 187.
Gill, S.: 1951,Proc. Cambridge Phil. Soc. 47, 96.
Hull, T. E., Enright, W. H., Fellen, B. M., and Sedwick, A. E.: 1972,SIAM J. Num. Anal. 9, 603.
Jackson, K. R., Enright, W. H., and Hull, T. E.: 1978,SIAM J. Num. Anal. 15, 618.
Kalvouridis, T. J.: 1987,Astrophys. Space Sci. 136, 21.
Kalvouridis, T. J.: 1986, Ph.D. Thesis, National Tech. Univ. of Athens.
Kalvouridis, T. J. and Mavraganis, A. G.: 1986,Symmetric Motions in the Equatorial Magnetic-Binary Problem (in press).
Kutta, W.: 1901,Z. Math. Phys. 46, 453.
Mavraganis, A. G.: 1978,Astrophys. Space Sci. 54, 305.
Merson, R. H.: 1957,Proc. of a Symposium on Data Processing, Weapons Res. Establishment Salisbury, South Australia.
Papageorgiou, G. S.: 1983,Int. J. Comput. Math. 13, 143.
Richardson, L. F.: 1927,Trans. Roy. Soc. London 226, 299.
Scraton, R. E.: 1984,Comp. J. 7, 246.
Shampine, L. F. and Watts, H. A.: 1971,Math. Comput. 25, 445.
Shintani, H.: 1966,J. Sci. Hiroshima Univ. Ser. A-1 Math. 30, 91.
Verner, J. H.: 1978,SIAM J. Num. Anal. 15, 772.
Verner, J. H.: 1979,SIAM J. Num. Anal. 16, 857.
Zonneveld, J. A.: 1964,Math. Centre Tracts, No. 8, Mathematische Centrum, Amsterdam MR 30, No. 1612.
Author information
Authors and Affiliations
Additional information
Section of Mechanics.
Section of Mathematics.
Rights and permissions
About this article
Cite this article
Kalvouridis, T., Papageorgiou, G. & Simos, T. A comparison of numerical integration methods in the equatorial magnetic-binary problem. Astrophys Space Sci 139, 21–35 (1987). https://doi.org/10.1007/BF00643810
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00643810