Symplectic P-stable Additive Runge--Kutta Methods
Numerical Analysis
2019-09-25 v1 Numerical Analysis
Symplectic Geometry
Abstract
Symplectic partitioned Runge--Kutta methods can be obtained from a variational formulation where all the terms in the discrete Lagrangian are treated with the same quadrature formula. We construct a family of symplectic methods allowing the use of different quadrature formulas (primary and secondary) for different terms of the Lagrangian. In particular, we study a family of methods using Lobatto quadrature (with corresponding Lobatto IIIA-B symplectic pair) as a primary method and Gauss--Legendre quadrature as a secondary method. The methods have the same favourable implicitness as the underlying Lobatto IIIA-B pair, and, in addition, they are \emph{P-stable}, therefore suitable for application to highly oscillatory problems.
Cite
@article{arxiv.1909.11017,
title = {Symplectic P-stable Additive Runge--Kutta Methods},
author = {Antonella Zanna},
journal= {arXiv preprint arXiv:1909.11017},
year = {2019}
}