Linearly implicit structure-preserving schemes for Hamiltonian systems

DOI10.1016/j.cam.2019.112489zbMath1456.65063arXiv1901.03573OpenAlexW2976658508WikidataQ127245556 ScholiaQ127245556MaRDI QIDQ2223801

Sølve Eidnes, Lu Li, Shun Sato

Publication date: 3 February 2021

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1901.03573

zbMATH Keywords

Korteweg-de Vries equationHamiltonian systemCamassa-Holm equationlinearly implicit methodsenergy preservation

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Numerical methods for Hamiltonian systems including symplectic integrators (65P10)

Related Items (10)

A new symmetric linearly implicit exponential integrator preserving polynomial invariants or Lyapunov functions for conservative or dissipative systems ⋮ Efficient energy-preserving exponential integrators for multi-component Hamiltonian systems ⋮ A linearly implicit structure-preserving scheme for the Camassa-Holm equation based on multiple scalar auxiliary variables approach ⋮ Structure-preserving reduced-order modeling of Korteweg-de Vries equation ⋮ Geometric Integration of ODEs Using Multiple Quadratic Auxiliary Variables ⋮ Linearly implicit methods for Allen-Cahn equation ⋮ Arbitrarily High-Order Energy-Preserving Schemes for the Camassa-Holm Equation Based on the Quadratic Auxiliary Variable Approach ⋮ A high-order linearly implicit energy-preserving Partitioned Runge-Kutta scheme for a class of nonlinear dispersive equations ⋮ Linear implicit finite difference methods with energy conservation property for space fractional Klein-Gordon-Zakharov system ⋮ Order theory for discrete gradient methods

Cites Work

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• A General Framework for Deriving Integral Preserving Numerical Methods for PDEs
• Geometric integration using discrete gradients
• Geometric properties of Kahan's method
• A new class of energy-preserving numerical integration methods
• Geometric Numerical Integration
• Dissipative or conservative finite-difference schemes for complex-valued nonlinear partial differential equations

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