000126417 001__ 126417 000126417 005__ 20241125101137.0 000126417 0247_ $$2doi$$a10.1007/s10569-023-10142-7 000126417 0248_ $$2sideral$$a133914 000126417 037__ $$aART-2023-133914 000126417 041__ $$aeng 000126417 100__ $$0(orcid)0000-0002-3312-5710$$aCalvo, M.$$uUniversidad de Zaragoza 000126417 245__ $$aOn the integral solution of elliptic Kepler’s equation 000126417 260__ $$c2023 000126417 5060_ $$aAccess copy available to the general public$$fUnrestricted 000126417 5203_ $$aIn a recent paper, Philcox, Goodman and Slepian obtain an explicit solution of the elliptic Kepler’s equation (KE) as a quotient of two contour integrals along a Jordan curve C=C(M,e) that contains the unique real solution of KE but not includes other complex zeros of KE in its interior. The aim of this paper is to study the main issues that arise in the practical implementation of this integral solution. Thus, after a study of the complex zeros of KE, several families of Jordan contours C=C(M,e) that are suitable for this integral solution are proposed. Since contours with minimal length turn out to be the more accurate for numerical purposes, several families that minimize their length are constructed. Secondly, the approximation of the contour integrals by the composite trapezoidal rule is considered. Recall that this rule is employed in the fast Fourier transform and, in spite of its lower order, displays a spectral convergence as a function of the number of nodes, which implies a very fast convergence. Finally, the results of some numerical experiments are presented to show that such a combination of appropriate contours with the composite trapezoidal rule leads to a powerful numerical method to solve KE with any desired accuracy for all values of eccentricity. 000126417 536__ $$9info:eu-repo/grantAgreement/ES/DGA/E41-20R$$9info:eu-repo/grantAgreement/ES/DGA-FSE/E24-20R$$9info:eu-repo/grantAgreement/ES/MICINN/PID2019-109045GB-C31$$9info:eu-repo/grantAgreement/ES/MICINN/PID2020-117066GB-I00 000126417 540__ $$9info:eu-repo/semantics/openAccess$$aby$$uhttp://creativecommons.org/licenses/by/3.0/es/ 000126417 590__ $$a1.6$$b2023 000126417 592__ $$a0.521$$b2023 000126417 591__ $$aMATHEMATICS, INTERDISCIPLINARY APPLICATIONS$$b70 / 135 = 0.519$$c2023$$dQ3$$eT2 000126417 593__ $$aApplied Mathematics$$c2023$$dQ2 000126417 591__ $$aASTRONOMY & ASTROPHYSICS$$b51 / 84 = 0.607$$c2023$$dQ3$$eT2 000126417 593__ $$aAstronomy and Astrophysics$$c2023$$dQ2 000126417 593__ $$aComputational Mathematics$$c2023$$dQ2 000126417 593__ $$aMathematical Physics$$c2023$$dQ2 000126417 593__ $$aModeling and Simulation$$c2023$$dQ2 000126417 593__ $$aSpace and Planetary Science$$c2023$$dQ3 000126417 594__ $$a3.0$$b2023 000126417 655_4 $$ainfo:eu-repo/semantics/article$$vinfo:eu-repo/semantics/publishedVersion 000126417 700__ $$0(orcid)0000-0001-5208-4494$$aElipe, A.$$uUniversidad de Zaragoza 000126417 700__ $$0(orcid)0000-0002-4238-3228$$aRández, L.$$uUniversidad de Zaragoza 000126417 7102_ $$12005$$2595$$aUniversidad de Zaragoza$$bDpto. Matemática Aplicada$$cÁrea Matemática Aplicada 000126417 773__ $$g135, 3 (2023), 26 [18 pp.]$$pCelest. mech. dyn. astron.$$tCelestial Mechanics and Dynamical Astronomy$$x0923-2958 000126417 8564_ $$s619862$$uhttps://zaguan.unizar.es/record/126417/files/texto_completo.pdf$$yVersión publicada 000126417 8564_ $$s1212902$$uhttps://zaguan.unizar.es/record/126417/files/texto_completo.jpg?subformat=icon$$xicon$$yVersión publicada 000126417 909CO $$ooai:zaguan.unizar.es:126417$$particulos$$pdriver 000126417 951__ $$a2024-11-22-12:01:11 000126417 980__ $$aARTICLE