Instituto de Investigación
en Matemáticas

No se ha especificado ningún tipo
No se ha especificado ningún tipo

On the choice of time‐transformation functions for adaptive

Ander Murua (Universidad del País Vasco)

Fecha: 15/12/2011 13:00
Lugar: Sala de Grados de la Facultad de Ciencias
Grupo: Departamento de Matemática Aplicada

It is well known that, when numerically integrating Hamiltonian systems by means of a symplectic integrator, standard variable step‐size implementation destroys the good long‐time behaviour of the numerical solution. However, constant step‐size implementation may be highly inefficient when numerically simulating a trajectory with large variations in the time‐scale (typically, when evolving near singularities of the Hamiltonian function). That difficulty can be overcome by applying a symplectic integrator with constant step‐size to a transformed Hamiltonian system that effectively applies a timetransformation of the form $dt/ d au = s( y) $. This requires an apriori choice of an appropriate function s( y) . In the present work, we obtain bounds of the local discretization errors of B‐series methods (including symplectic Runge‐Kutta methods) and try to use them to choose appropriate timetransformation functions s( y) . We apply the main ideas to construct suitable time‐transformation functions s( y) for N‐body systems.