On the Arbitrarily Long-Term Stability of Conservative Methods

DOI10.1137/16M1085929zbMath1405.65085arXiv1607.06160OpenAlexW3102238642MaRDI QIDQ5376445

Jean-Christophe Nave, Andy T. S. Wan

Publication date: 18 September 2018

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

Full work available at URL: https://arxiv.org/abs/1607.06160

zbMATH Keywords

tolerancediscretizationconservative methodsfinite differencelong-term stabilitytopological spacemultiplier methodautonomous systemnormal spaceBrouwer's lawconsistencemachine precision

Mathematics Subject Classification ID

Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for initial value problems involving ordinary differential equations (65L05) Error bounds for numerical methods for ordinary differential equations (65L70) Numerical methods for Hamiltonian systems including symplectic integrators (65P10) Finite difference and finite volume methods for ordinary differential equations (65L12) Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems (37M15)

Related Items (4)

Conservative integrators for many-body problems ⋮ Conservative integrators for vortex blob methods on the plane ⋮ Conservative integrators for piecewise smooth systems with transversal dynamics ⋮ Area-preserving geometric Hermite interpolation

Cites Work

• Achieving Brouwer's law with implicit Runge-Kutta methods
• Exact energy-momentum conserving algorithms and symplectic schemes for nonlinear dynamics
• Energy and momentum conserving methods of arbitrary order for the numerical integration of equations of motion. I: Motion of a single particle
• On the Hamiltonian interpolation of near-to-the-identity symplectic mappings with application to symplectic integration algorithms
• Accurate long-term integration of dynamical systems
• Volume-preserving algorithms for source-free dynamical systems
• Round-off error in long-term orbital integrations using multistep methods
• Preserving energy resp. dissipation in numerical PDEs using the ``Average Vector Field method
• Analysis of Hamiltonian boundary value methods (HBVMs): A class of energy-preserving Runge-Kutta methods for the numerical solution of polynomial Hamiltonian systems
• Time integration and discrete Hamiltonian systems
• Stability of Runge-Kutta Methods for Trajectory Problems
• Discrete Variational Derivative Method
• Preserving multiple first integrals by discrete gradients
• Topics in structure-preserving discretization
• A General Framework for Deriving Integral Preserving Numerical Methods for PDEs
• The Development of Variable-Step Symplectic Integrators, with Application to the Two-Body Problem
• Simulating Hamiltonian Dynamics
• Discrete mechanics and variational integrators
• Finite element exterior calculus, homological techniques, and applications
• Geometric integration using discrete gradients
• Discrete gradient methods for solving ODEs numerically while preserving a first integral
• Integral-preserving integrators
• Finite Difference Calculus Invariant Structure of a Class of Algorithms for the Nonlinear Klein–Gordon Equation
• Energy-preserving Runge-Kutta methods
• Conservative Methods for Dynamical Systems
• A new class of energy-preserving numerical integration methods
• Geometric Numerical Integration
• On the Partial Difference Equations of Mathematical Physics
• Geometric foundations of numerical algorithms and symmetry
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