A family of multistep methods to integrate orbits on spheres
type: Item
instance of: scholarly article
title: A family of multistep methods to integrate orbits on spheres
zbMATH Open document ID: 0791.65057
DOI: 10.1007/BF01385753
published in: Numerische Mathematik
publication date: 1994-07-07T00:00:00Z
full work available at URL: https://eudml.org/doc/133736
review text: A trajectory problem is an initial value problem where the interest lies in obtaining the curve traced by the solution, rather than in finding the actual correspondence between the values of the parameter and the points on that curve. This paper introduces a family of multistep numerical methods to integrate trajectory problems whose solution is on a spherical surface. It is shown that this kind of algorithms has good numerical properties: consistency, stability, convergence and others that are not standard such as preserving the surface and being sensitive to the geodesic curvature of the solution. The latest ones make them a better choice for certain problems. To illustrate the good behaviour of these algorithms we present an example in which the Kepler problem is integrated.
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 569159
zbMATH Keywords: multistep methods
zbMATH Keywords: orbits on spheres
zbMATH Keywords: trajectory problem
zbMATH Keywords: initial value problem
zbMATH Keywords: algorithms
zbMATH Keywords: consistency
zbMATH Keywords: stability
zbMATH Keywords: convergence
zbMATH Keywords: Kepler problem
author: José M. Ferrándiz
author: María-Teresa Pérez
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 569159