Order conditions for canonical Runge-Kutta schemes
SIAM Journal on Numerical Analysis
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Symplectic partitioned Runge-Kutta methods for constrained Hamiltonian systems
SIAM Journal on Numerical Analysis
A new look at finite elements in time: a variational interpretation of Runge-Kutta methods
Applied Numerical Mathematics
Numerical Integrators that Preserve Symmetries and Reversing Symmetries
SIAM Journal on Numerical Analysis
The Midpoint Scheme and Variants for Hamiltonian Systems: Advantages and Pitfalls
SIAM Journal on Scientific Computing
Multi-symplectic Runge-Kutta collocation methods for Hamiltonian wave equations
Journal of Computational Physics
Multisymplectic box schemes and the Korteweg-de Vries equation
Applied Numerical Mathematics - Special issue: Workshop on innovative time integrators for PDEs
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
A New Implementation of Symplectic Runge-Kutta Methods
SIAM Journal on Scientific Computing
SIAM Journal on Numerical Analysis
On the multisymplecticity of partitioned Runge-Kutta and splitting methods
International Journal of Computer Mathematics - Splitting Methods for Differential Equations
On Multisymplecticity of Partitioned Runge-Kutta Methods
SIAM Journal on Scientific Computing
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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, ${tr}M_s$, 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 ${tr}M_s(\omega)$ as a function of the frequency $\omega$ and stage number $s$.