Linear stability of partitioned runge-kutta methods

摘要

We study the linear stability of partitioned Runge-Kutta (PRK) methods applied to linear separable Hamiltonian ODEs and to the semidiscretization of certain Hamiltonian PDEs. We extend the work of Jay and Petzold [Highly Oscillatory Systems and Periodic Stability, Preprint 95-015, Army High Performance Computing Research Center, Stanford, CA, 1995] by presenting simplified expressions of the trace of the stability matrix, trMs, for the Lobatto IIIA-IIIB family of symplectic PRK methods. By making the connection to Padé approximants and continued fractions, we study the asymptotic behavior of trMs(ω) as a function of the frequency ω and stage number s.