[Todos CMAT] charla de Raúl Tempone. Resol. numérica de ecs diferenciales ordinarias

[Dr. Roberto Markarian]

(ruego a AViola y PMonzón que distribuyan en sus institutos)

Viernes 29 de diciembre, 10 hs.

Estimacion del error global en ODEs y metodos adaptativos para su control.

> Resumen:
> A variational principle, inspired by optimal control, yields a simple
> derivation of an error representation, global error=\sum local
> error*weight, for general approximation of functions of solutions to
> ordinary differential equations. This error representation is then
> approximated by a sum of computable error indicators, to obtain a useful
> global error indicator for adaptive mesh refinements. A uniqueness
> formulation is provided for desirable error representations of adaptive
> algorithms.
> We construct an adaptive algorithm for ordinary differential equations and
> analyze its asymptotic behavior as the error tolerance parameter tends to
> zero. An adaptive algorithm, based on the error indicators and successive
> subdivision of time steps, is proven to stop with the optimal number, N,
> of steps up to a problem independent factor defined in the algorithm.