Order conditions for RKN methods solving general second-order oscillatory systems

DOI10.1007/s11075-013-9728-5zbMath1292.65083OpenAlexW2049431512MaRDI QIDQ2453475

Xiong You, Jinxi Zhao, Hongli Yang, Yong Lei Fang, Xin-Yuan Wu

Publication date: 6 June 2014

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-013-9728-5

zbMATH Keywords

order conditionsextended Nyström treesextended Runge-Kutta-Nyström-type methodssecond-order oscillatory systems

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations (34C10) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06)

Related Items (20)

Modified multi-step Nyström methods for oscillatory general second-order initial value problems ⋮ Multi-step Nyström methods for general second-order initial value problemsy″(t) =f(t,y(t),y′(t)) ⋮ Symplectic and symmetric trigonometrically-fitted ARKN methods ⋮ A new collocation formulation for the block Falkner-type methods with trigonometric coefficients for oscillatory second order ordinary differential equations ⋮ An improved tri-coloured rooted-tree theory and order conditions for ERKN methods for general multi-frequency oscillatory systems ⋮ A feasible and effective technique in constructing ERKN methods for multi-frequency multidimensional oscillators in scientific computation ⋮ A variable step-size implementation of the hybrid Nyström method for integrating Hamiltonian and stiff differential systems ⋮ A novel class of explicit divergence-free time-domain methods for efficiently solving Maxwell's equations ⋮ The construction of arbitrary order ERKN methods based on group theory for solving oscillatory Hamiltonian systems with applications ⋮ Two-derivative Runge-Kutta-Nyström methods for second-order ordinary differential equations ⋮ An approximate Lax-Wendroff-type procedure for high order accurate schemes for hyperbolic conservation laws ⋮ Oscillation-preserving algorithms for efficiently solving highly oscillatory second-order ODEs ⋮ On modified TDRKN methods for second-order systems of differential equations ⋮ Stability analysis for explicit ERKN methods solving general second-order oscillatory systems ⋮ A class of linear multi-step method adapted to general oscillatory second-order initial value problems ⋮ Symmetric collocation ERKN methods for general second-order oscillators ⋮ Trigonometrically fitted two-derivative Runge-Kutta-Nyström methods for second-order oscillatory differential equations ⋮ An approach to solving Maxwell's equations in time domain ⋮ The tri-coloured free-tree theory for symplectic multi-frequency ERKN methods ⋮ An explicit trigonometrically fitted Runge–Kutta method for stiff and oscillatory problems with two frequencies

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