Order theory for discrete gradient methods
From MaRDI portal
Publication:2100535
DOI10.1007/s10543-022-00909-zOpenAlexW4210828370MaRDI QIDQ2100535
Publication date: 22 November 2022
Published in: BIT (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2003.08267
Artificial neural networks and deep learning (68T07) Numerical methods for initial value problems involving ordinary differential equations (65L05) Numerical methods for Hamiltonian systems including symplectic integrators (65P10) Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems (37M15)
Related Items (1)
Uses Software
Cites Work
- Unnamed Item
- Discrete gradient methods for preserving a first integral of an ordinary differential equation
- The discrete variational derivative method based on discrete differential forms
- Projection methods and discrete gradient methods for preserving first integrals of ODEs
- Linear energy-preserving integrators for Poisson systems
- Adaptive energy preserving methods for partial differential equations
- Hamiltonian-conserving discrete canonical equations based on variational difference quotients
- Order conditions for Rosenbrock type methods
- A conservative difference scheme for a system of Hamiltonian equations with external action
- A fourth-order AVF method for the numerical integration of sine-Gordon equation
- Spatially accurate dissipative or conservative finite difference schemes derived by the discrete variational method
- Finite difference schemes for \(\frac{\partial u}{\partial t}=(\frac{\partial}{\partial x})^\alpha\frac{\delta G}{\delta u}\) that inherit energy conservation or dissipation property
- Energy-preserving exponential integrators of arbitrarily high order for conservative or dissipative systems with highly oscillatory solutions
- Linearly implicit structure-preserving schemes for Hamiltonian systems
- Preserving energy resp. dissipation in numerical PDEs using the ``Average Vector Field method
- An algebraic approach to invariant preserving integators: the case of quadratic and Hamiltonian invariants
- Time integration and discrete Hamiltonian systems
- Energy conservation with non-symplectic methods: examples and counter-examples
- Two Energy-Conserved Splitting Methods for Three-Dimensional Time-Domain Maxwell's Equations and the Convergence Analysis
- Discrete Variational Derivative Method
- A General Framework for Deriving Integral Preserving Numerical Methods for PDEs
- On Upstream Differencing and Godunov-Type Schemes for Hyperbolic Conservation Laws
- Lectures on Mechanics
- Product formulas and numerical algorithms
- Geometric integration using discrete gradients
- Integral-preserving integrators
- Energy-preserving Runge-Kutta methods
- Energy-preserving methods on Riemannian manifolds
- A new class of energy-preserving numerical integration methods
- Geometric Numerical Integration
- B-series and Order Conditions for Exponential Integrators
- Dissipative or conservative finite-difference schemes for complex-valued nonlinear partial differential equations
This page was built for publication: Order theory for discrete gradient methods
