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

DOI10.1016/j.cnsns.2014.10.015zbMath1329.65304OpenAlexW4242133629MaRDI QIDQ907195

Luigi Brugnano, Felice Iavernaro, Donato Trigiante

Publication date: 25 January 2016

Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cnsns.2014.10.015

zbMATH Keywords

collocation methodsRunge-Kutta methodsenergy-preserving methods

Mathematics Subject Classification ID

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

Related Items

Geometric Integration of ODEs Using Multiple Quadratic Auxiliary Variables, Energy-preserving methods for Poisson systems, Line integral methods which preserve all invariants of conservative problems, Low rank Runge-Kutta methods, symplecticity and stochastic Hamiltonian problems with additive noise, The lack of continuity and the role of infinite and infinitesimal in numerical methods for ODEs: the case of symplecticity, A simple framework for the derivation and analysis of effective one-step methods for ODEs, A note on the efficient implementation of Hamiltonian BVMs, Structure-preserving Runge-Kutta methods for stochastic Hamiltonian equations with additive noise, A two-step, fourth-order method with energy preserving properties

Cites Work

• A note on the efficient implementation of Hamiltonian BVMs
• An algebraic approach to invariant preserving integators: the case of quadratic and Hamiltonian invariants
• Energy conservation with non-symplectic methods: examples and counter-examples
• Simulating Hamiltonian Dynamics
• On the Preservation of Invariants by Explicit Runge--Kutta Methods
• Geometric integration using discrete gradients
• Energy-preserving Runge-Kutta methods
• A new class of energy-preserving numerical integration methods
• Geometric Numerical Integration
• s-stage Trapezoidal Methods for the Conservation of Hamiltonian Functions of Polynomial Type
• Hamiltonian BVMs (HBVMs): A Family of “Drift Free” Methods for Integrating polynomial Hamiltonian problems
• Hamiltonian BVMs (HBVMs): Implementation Details and Applications
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