Astronomy and Astrophysics – Astronomy
Scientific paper
Aug 2002
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2002mnras.334..855p&link_type=abstract
Monthly Notices of the Royal Astronomical Society, Volume 334, Issue 4, pp. 855-858.
Astronomy and Astrophysics
Astronomy
5
Gravitational Waves, Methods: Analytical, Methods: Numerical, Celestial Mechanics, Binaries: General
Scientific paper
The exact solution for any eccentricity of the Peters-Mathews model of binary stars emitting gravitational waves leads to hypergeometric functions of Appell and Gauss type. Efficient (fast and accurate) numerical computations of such functions can be obtained by using the Padé approximation. Padé rational approximants, for equal numbers of coefficients, are more accurate than Taylor series representation. Unfortunately, the algorithm computing Padé coefficients numerically from Taylor series is known to be unstable. This numerical instability lowers the accuracy of the Padé approximant. In this paper, double precision accuracy Padé approximant coefficients are computed symbolically. Advantages of the symbolic computation with respect to the numerical treatment are shown, providing accurate representations of the Appell and Gauss hypergeometric functions. The symbolic approach can be extended to higher post-Newtonian models.
Pierro Vincenzo
Pinto Innocenzo M.
Spallicci di D. A. M. A. F.
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