133402 20260217205510.0 doi 10.1007/s10569-024-10184-5 sideral 138074 ART-2024-138074 eng Calvo, M. (orcid)0000-0002-3312-5710 On the integral solution of hyperbolic Kepler’s equation 2024 Access copy available to the general public Unrestricted In a recent paper of Philcox, Goodman and Slepian, the solution of the elliptic Kepler’s equation is given as a quotient of two contour integrals along a Jordan curve that contains in its interior the unique real solution of the elliptic Kepler’s equation and does not include other complex zeroes. In this paper, we show that a similar explicit integral solution can be given for the hyperbolic Kepler’s equation. With this purpose, we carry out a study of the complex zeros of the hyperbolic Kepler’s equation in order to define suitable Jordan contours in the integrals. Even more, we show that appropriate elliptic Jordan contours can be defined for such integrals, which reduces the computing time. Moreover, using the ideas behind the fast Fourier transform (FFT) algorithm, these integrals can be approximated by the composite trapezoidal rule which gives an algorithm with spectral convergence as a function of the number of nodes. The results of some numerical experiments are presented to show that this implementation is a reliable and very accurate algorithm for solving the hyperbolic Kepler’s equation. info:eu-repo/semantics/openAccess by https://creativecommons.org/licenses/by/4.0/deed.es 1.4 2024 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS 84 / 136 = 0.618 2024 Q3 T2 ASTRONOMY & ASTROPHYSICS 54 / 84 = 0.643 2024 Q3 T2 0.448 2024 Applied Mathematics 2024 Q2 Computational Mathematics 2024 Q2 Modeling and Simulation 2024 Q2 Mathematical Physics 2024 Q3 Space and Planetary Science 2024 Q3 Astronomy and Astrophysics 2024 Q3 2.8 2024 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion Elipe, A. Universidad de Zaragoza (orcid)0000-0001-5208-4494 Rández, L. Universidad de Zaragoza (orcid)0000-0002-4238-3228 2005 595 Universidad de Zaragoza Dpto. Matemática Aplicada Área Matemática Aplicada 136, 2 (2024), 13 [14 pp.] Celest. mech. dyn. astron. Celestial Mechanics and Dynamical Astronomy 0923-2958 614641 http://zaguan.unizar.es/record/133402/files/texto_completo.pdf Versión publicada 1161951 http://zaguan.unizar.es/record/133402/files/texto_completo.jpg?subformat=icon icon Versión publicada oai:zaguan.unizar.es:133402 articulos driver 2026-02-17-20:24:53 ARTICLE