An Efficient Integrator that Uses Gauss-Radau Spacings
This describes our integrator RADAU, which has been used by several groups in the U.S.A., in Italy, and in the U.S.S.R, over the past 10 years in the numerical integration of orbits and other problems involving numerical solution of systems of ordinary differential equations. First- and second-order equations are solved directly, including the general second-order case. A self-starting integrator, RADAU proceeds by sequences within which the substeps are taken at Gauss-Radau spacings. This allows rather high orders of accuracy with relatively few function evaluations. After the first sequence the information from previous sequences is used to improve the accuracy. The integrator itself chooses the next sequence size. When a 64-bit double word is available in double precision, a 15th-order version is often appropriate, and the FORTRAN code for this case is included here. RADAU is at least comparable with the best of other integrators in speed and accuracy, and it is often superior, particularly at high accuracies.
Unable to display preview. Download preview PDF.
- Batrakov, Yu. N .:1982, ‘Methods of Computation of the Perturbed Motion of Small Bodies in the Solar System’ inSun and Planetary System, (Proceedings of the VI European Meeting in Astronomy), W. Fricke and G. Teleki, editors, D. Reidel Publishing Co., Dordrecht. pp415–419Google Scholar
- Bettis, D. G. and Szebehely, V.: 1972, ‘Treatment of Close Approaches in the Numerical Integration of the Gravitational Problem of N-bodies’ Gravitational N-Body Problem, M. Lecar, editor, D. Reidel Publishing Co., Dordrecht, pp388–405. See p395Google Scholar
- Carusi, A., Kresak, L., Perozzi, E., and Valsecchi, G. B.: 1985 ‘The Long-Term Evolution Project’ inDynamics of Comets: Their Origin and Evolution, A. Carusi and G.B. Valsecchi, editors, D. Reidel Publishing Co., Dordrecht. (IAU Colloq. 83, Rome, June 1984 ) This volumeGoogle Scholar
- Eckert, W. J., Brouwer, D., and Clemence, G. M. : 1951 ‘Coordinates of the Five Outer Planets, 1653–2060’Astron. Papers Am. Ephemeris,12 Google Scholar
- Everhart, E.: 1974b ‘An Efficient Integrator of Very High Order and Accuracy’ Denver Res. Inst. Tech. Report, 1 July 1974 (unpublished)Google Scholar
- Fehlberg, E.: 1972, ‘Classical Eighth- and Lower Order Runge-Kutta-Nystrom Formulas with Stepsize Control for Special Second-Order Differential Equations’,NASA Tech. Rept., NASA TR R-381Google Scholar
- Gallaher, L. J. and Perlin, I. E.: 1966. E.: 1966, ‘A comparison of Several Methods of Numerical Integration of Nonlinear Differential Equations’. Presented at the SIAM meeting, Univ. of Iowa, March. 1966 (unpublished). See Krogh, 1973.Google Scholar
- Levi-Civita, T.: 1903, ‘Traiettorie singulars ed arts nel problems ristretto del tre corp’,Annali di Mat.9, pp1–32Google Scholar
- Shefer, V.A.: 1982, ‘Variational Equations of the Perturbed Two Body Problem in Regularized Form’, Institute of Theoretical Astronomy, Leningrad. Publication Na.37. An 11th-order version of RADAR is usedGoogle Scholar