Presented by:
Antonella Zanna
Date:
Wednesday 11th December 2019 - 14:05 to 14:50
Venue:
INI Seminar Room 2
Event:
Abstract:
Symplectic partitioned Runge–Kutta methods can be
obtained from a variational formulation treating all the terms in the
Lagrangian with the same quadrature formula. We construct a family of
symplectic methods allowing the use of different quadrature formula for
different parts of the Lagrangian. In particular, we study a family of methods
using Lobatto quadrature (with corresponding Lobatto IIIA-IIIB symplectic
method) and Gauss–Legendre quadrature combined in an appropriate way. The
resulting methods are similar to additive Runge-Kutta methods. The IMEX method,
using the Verlet and IMR combination is a particular case of this family.
The methods have the same favourable implicitness as the
underlying Lobatto IIIA-IIIB pair. Differently from the Lobatto IIIA-IIIB,
which are known not to be P-stable, we show that the new methods satisfy the
requirements for P-stability.
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