On the preservation of second integrals by Runge-Kutta methods

DOI10.3934/jcd.2023001zbMath1526.37088arXiv2105.10929OpenAlexW3164758163MaRDI QIDQ6111237

Benjamin K. Tapley

Publication date: 6 July 2023

Published in: Journal of Computational Dynamics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2105.10929

zbMATH Keywords

dynamical systemsRunge-Kutta methodsdiscrete dynamical systemsDarboux polynomialssecond integrals

Mathematics Subject Classification ID

Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Discrete version of topics in analysis (39A12) Numerical methods for Hamiltonian systems including symplectic integrators (65P10) Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems (37M15) Integrable difference and lattice equations; integrability tests (39A36) Completely integrable discrete dynamical systems (37J70)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Equations de Pfaff algébriques
• On the nonexistence of constants of derivations: the proof of a theorem of Jouanolou and its development
• Volume-preserving algorithms for source-free dynamical systems
• Algebraic conditions for a centre or a focus in some simple systems of arbitrary degree
• Detecting and determining preserved measures and integrals of birational maps
• Efficient energy-preserving integrators for oscillatory Hamiltonian systems
• Lie-Poisson Hamilton-Jacobi theory and Lie-Poisson integrators
• Stability of Runge-Kutta Methods for Trajectory Problems
• Preserving multiple first integrals by discrete gradients
• Simulating Hamiltonian Dynamics
• Diagonal Padé Approximations for Initial Value Problems
• Algorithms for special integrals of ordinary differential equations
• Geometric properties of Kahan's method
• Using discrete Darboux polynomials to detect and determine preserved measures and integrals of rational maps
• Solving Ordinary Differential Equations II
• Energy-preserving Runge-Kutta methods
• A new class of energy-preserving numerical integration methods
• Geometric Numerical Integration
• Solving ODEs numerically while preserving a first integral

This page was built for publication: On the preservation of second integrals by Runge-Kutta methods