Astronomy and Astrophysics – Astronomy
Scientific paper
Feb 1978
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1978pazh....4...34e&link_type=abstract
(Pis'ma v Astronomicheskii Zhurnal, vol. 4, Jan. 1978, p. 34-37.) Soviet Astronomy Letters, vol. 4, Jan.-Feb. 1978, p. 18-20. Tr
Astronomy and Astrophysics
Astronomy
Gravitational Effects, Numerical Integration, Two Body Problem, Astronomical Models, Difference Equations, Error Analysis
Scientific paper
A modification of Cowell's difference method is outlined in which the difference equation is solved by the method of horizontal successive approximations. The behavior of the absolute error in the modified method is examined using examples of solutions to the two-body problem in a Newtonian gravitational field for the case of elliptical motion; the specific cases of the Jupiter-sun and earth-sun systems are considered. The calculations show that the behavior of the absolute error is most stable if the convergence condition of the method of horizontal successive approximations is satisfied, that the accuracy of the choice of initial values for the relevant parameters has little effect on the absolute error, and that rounding errors are the main source of the absolute error. The efficiency of the proposed modification is demonstrated by comparisons with results obtained by the 'standard' method for solving Cowell's difference equation and by the fourth-order Runge-Kutta method.
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