On the numerical integration of an explicit solution of the homologous collapse’s radial evolution in time

Calvo, Manuel (Universidad de Zaragoza) ; Elipe, Antonio (Universidad de Zaragoza) ; Rández, Luis (Universidad de Zaragoza)

Resumen: In a recent paper, Slepian and Philcox derive an explicit solution of the homologous collapse from rest of a uniform density sphere under its self-gravity as a function of time. Their solution is given in terms of two curvilinear integrals along a suitable Jordan contour; in practice, it must be approximated by a quadrature rule. The aim of this paper is to examine how the choice of the contour and the quadrature rule affects the accuracy and the efficiency of this integral solution approximation. More precisely, after a study of the complex roots of a transcendental equation that relates time with the variable, some alternative Jordan contours that turn out to be more convenient are proposed. Then, by using as quadrature rule the composite trapezoidal rule because of its reliability and spectral convergence accuracy, some numerical experiments are presented to show that the combination of contours and quadrature rule allows us to obtain numerical results with high accuracy and low computational cost.

Idioma: Inglés

DOI: 10.1093/mnras/stac1418

Año: 2022

Publicado en: MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY 514, 1 (2022), 1258-1265
ISSN: 0035-8711

Factor impacto JCR: 4.8 (2022)

Categ. JCR: ASTRONOMY & ASTROPHYSICS rank: 17 / 69 = 0.246 (2022) - Q1 - T1

Factor impacto CITESCORE: 9.5 - Earth and Planetary Sciences (Q1) - Physics and Astronomy (Q1)

Factor impacto SCIMAGO: 1.734 - Space and Planetary Science (Q1) - Astronomy and Astrophysics (Q1)

Financiación: info:eu-repo/grantAgreement/ES/DGA-FSE/E24-20R
Financiación: info:eu-repo/grantAgreement/ES/DGA-FSE/E41-20R
Financiación: info:eu-repo/grantAgreement/ES/MICINN/PID2019-109045GB-C31
Financiación: info:eu-repo/grantAgreement/ES/MICINN/PID2020-117066GB-I00

Tipo y forma: Article (Published version)

Área (Departamento): Área Matemática Aplicada (Dpto. Matemática Aplicada)