Linear Stability of Partitioned Runge–Kutta Methods

DOI10.1137/100787234zbMath1228.65124OpenAlexW2067344577MaRDI QIDQ3091799

P. S. P. Tse, Ya-Juan Sun, Robert I. Mclachlan

Publication date: 14 September 2011

Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/100787234

zbMATH Keywords

asymptotic behaviorlinear stabilityHamiltonian systemsPadé approximantsnonlinear wave equationcontinued fractionsstability regionharmonic oscillatorpartitioned Runge-Kutta methodsLobatto IIIA-IIIB methodstrace of stability matrix

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Asymptotic expansions of solutions to ordinary differential equations (34E05)

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Two Novel Classes of Arbitrary High-Order Structure-Preserving Algorithms for Canonical Hamiltonian Systems ⋮ Symplectic P-stable additive Runge-Kutta methods ⋮ Construction and comparison of multidimensional spectral variational integrators and spectral collocation methods ⋮ Parallelization, initialization, and boundary treatments for the diamond scheme ⋮ Multisymplecticity of hybridizable discontinuous Galerkin methods ⋮ Meshless symplectic and multi-symplectic local RBF collocation methods for Hamiltonian PDEs ⋮ Partitioned second derivative methods for separable Hamiltonian problems ⋮ Travelling wave solutions of multisymplectic discretizations of semi-linear wave equations ⋮ The Multisymplectic Diamond Scheme

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