Continuous-Stage Runge-Kutta approximation to Differential Problems
arXiv:2203.11189 · doi:10.3390/axioms11050192
Abstract
In recent years, the efficient numerical solution of Hamiltonian problems has led to the definition of a class of energy-conserving Runge-Kutta methods named Hamiltonian Boundary Value Methods (HBVMs). Such methods admit an interesting interpretation in terms of continuous-stage Runge-Kutta methods, which is here recalled and revisited for general differential problems.
arXiv comment20 pages
References in corpus (16)
- A unifying framework for the derivation and analysis of effective classes of one-step methods for ODEs
- A note on the efficient implementation of Hamiltonian BVMs
- A characterization of energy-preserving methods and the construction of parallel integrators for Hamiltonian systems
- Spectrally accurate space-time solution of Hamiltonian PDEs
- On the effectiveness of spectral methods for the numerical solution of multi-frequency highly-oscillatory Hamiltonian problems
- Multiple invariants conserving Runge-Kutta type methods for Hamiltonian problems
- High-order energy-conserving Line Integral Methods for charged particle dynamics
- Arbitrarily high-order energy-preserving methods for simulating the gyrocenter dynamics of charged particles
- A Two Step, Fourth Order, Nearly-Linear Method with Energy Preserving Properties
- Analysis of Spectral Hamiltonian Boundary Value Methods (SHBVMs) for the numerical solution of ODE problems
- Energy-conserving methods for Hamiltonian Boundary Value Problems and applications in astrodynamics
- Line Integral solution of Hamiltonian PDEs
- A note on the continuous-stage Runge-Kutta-(Nyström) formulation of Hamiltonian Boundary Value Methods (HBVMs)
- Arbitrarily high-order energy-conserving methods for Poisson problems
- Line Integral Solution of Hamiltonian Systems with Holonomic Constraints
- Spectrally accurate space-time solution of Manakov systems