Discrete gradient methods have an energy conservation law
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Publication:379787
DOI10.3934/dcds.2014.34.1099zbMath1282.65112arXiv1302.4513OpenAlexW2962766945MaRDI QIDQ379787
Robert I. Mclachlan, Gilles Reinout Willem Quispel
Publication date: 11 November 2013
Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1302.4513
Hyperbolic conservation laws (35L65) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20)
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Cites Work
- \(A\)-stable Runge-Kutta methods for semilinear evolution equations
- The discrete energy-momentum method. Conserving algorithms for nonlinear elastodynamics
- A variational complex for difference equations
- Preserving energy resp. dissipation in numerical PDEs using the ``Average Vector Field method
- Time integration and discrete Hamiltonian systems
- On the multisymplecticity of partitioned Runge–Kutta and splitting methods
- Geometric integration using discrete gradients
- On the derivation of fluxes for conservation laws in Hamiltonian systems
- Discrete gradient methods for solving ODEs numerically while preserving a first integral
- A new class of energy-preserving numerical integration methods
- Numerical methods for Hamiltonian PDEs
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