Symplectic P-stable Additive Runge--Kutta Methods

2019/09/24 by Zanna, Antonella
#37J05 #65L06 #70H15 #FOS: Mathematics #Numerical Analysis (math.NA) #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.1909.11017

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 P-stable, therefore suitable for application to highly oscillatory problems.

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