Geometric Integration of ODEs Using Multiple Quadratic Auxiliary Variables

DOI10.1137/21M1442644zbMath1497.65256arXiv2108.06548OpenAlexW4292635709WikidataQ114073976 ScholiaQ114073976MaRDI QIDQ5099869

Benjamin K. Tapley

Publication date: 26 August 2022

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2108.06548

zbMATH Keywords

Runge-Kutta methodsenergy preservationstructure preservationdiscrete gradientsaverage vector fieldintegral preservation

Mathematics Subject Classification ID

Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Numerical methods for Hamiltonian systems including symplectic integrators (65P10)

Related Items (8)

Reduced-order modeling for Ablowitz-Ladik equation ⋮ On convergence of a novel linear conservative scheme for the two-dimensional fractional nonlinear Schrödinger equation with wave operator ⋮ Arbitrary high-order structure-preserving methods for the quantum Zakharov system ⋮ Arbitrarily high-order energy-preserving schemes for the Zakharov-Rubenchik equations ⋮ High-order Runge-Kutta structure-preserving methods for the coupled nonlinear Schrödinger-KdV equations ⋮ Arbitrary High-Order Structure-Preserving Schemes for Generalized Rosenau-Type Equations ⋮ An extended quadratic auxiliary variable method for the singular Lennard-Jones droplet liquid film model ⋮ Linearly implicit methods for Allen-Cahn equation

Cites Work

• Unnamed Item
• An energy-preserving exponentially-fitted continuous stage Runge-Kutta method for Hamiltonian systems
• Projection methods and discrete gradient methods for preserving first integrals of ODEs
• Some new structure-preserving algorithms for general multi-symplectic formulations of Hamiltonian PDEs
• Relaxation Runge-Kutta methods for Hamiltonian problems
• Reprint of ``Analysis of Hamiltonian boundary value methods (HBVMs): a class of energy-preserving Runge-Kutta methods for the numerical solution of polynomial Hamiltonian systems
• Hamiltonian-conserving discrete canonical equations based on variational difference quotients
• The problem of integrable discretization: Hamiltonian approach
• The scalar auxiliary variable (SAV) approach for gradient flows
• Preserving algebraic invariants with Runge-Kutta methods
• Scalar auxiliary variable approach for conservative/dissipative partial differential equations with unbounded energy functionals
• Linearly implicit structure-preserving schemes for Hamiltonian systems
• General local energy-preserving integrators for solving multi-symplectic Hamiltonian PDEs
• Preserving energy resp. dissipation in numerical PDEs using the ``Average Vector Field method
• Time integration and discrete Hamiltonian systems
• Stability of Runge-Kutta Methods for Trajectory Problems
• Discrete Variational Derivative Method
• A General Framework for Deriving Integral Preserving Numerical Methods for PDEs
• Geometric integration using discrete gradients
• On the Numerical Integration of Ordinary Differential Equations by Symmetric Composition Methods
• Spatial discretization of partial differential equations with integrals
• Unified Approach to Hamiltonian Systems, Poisson Systems, Gradient Systems, and Systems with Lyapunov Functions or First Integrals
• Energy-preserving Runge-Kutta methods
• Numerical approximations for a three-component Cahn–Hilliard phase-field model based on the invariant energy quadratization method
• The minimal stage, energy preserving Runge–Kutta method for polynomial Hamiltonian systems is the averaged vector field 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

This page was built for publication: Geometric Integration of ODEs Using Multiple Quadratic Auxiliary Variables