A family of multistep methods to integrate orbits on spheres
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.
scientific article; zbMATH DE number 569159