Cheap one-step global error estimation for odes

  1. Murua, A.
  2. Makazaga, J.
Revista:
New Zealand Journal of Mathematics

ISSN: 1179-4984

Any de publicació: 2000

Volum: 29

Pàgines: 211-221

Tipus: Article

GOOGLE SCHOLAR

Altres publicacions en: New Zealand Journal of Mathematics

Resum

We propose a class of one-step integrators for ODEs that provide an estimation of the global error along with the numerical solution. The schemes that we propose can be considered as a generalization of the globally embedded R K methods of Dormand, Gilmore and Prince . We present preliminary numerical experiments testing a particular 5th order scheme that we have constructed based on an optimized standard RK method. The numerical results seem to indicate that our method gives useful information on the behaviour of the global error while being practically as efficient as the underlying standard R K scheme.