Line integral methods which preserve all invariants of conservative problems

DOI10.1016/J.CAM.2012.03.026zbMath1246.65108arXiv1301.2367OpenAlexW2066954616MaRDI QIDQ433930

Felice Iavernaro, Luigi Brugnano

Publication date: 9 July 2012

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1301.2367

zbMATH Keywords

collocation methodnumerical experimentspolynomial Hamiltonian systemsHamiltonian boundary value methodsconservative problemsenergy-preserving methodsline integral methodsone-step methods

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Numerical methods for initial value problems involving ordinary differential equations (65L05) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60)

Related Items (23)

Drift-preserving numerical integrators for stochastic Poisson systems ⋮ Numerical methods for non conservative perturbations of conservative problems ⋮ Functionally-fitted energy-preserving integrators for Poisson systems ⋮ Spectrally accurate space-time solution of Manakov systems ⋮ A feasible and effective technique in constructing ERKN methods for multi-frequency multidimensional oscillators in scientific computation ⋮ Arbitrarily high-order energy-conserving methods for Poisson problems ⋮ High-order Runge-Kutta structure-preserving methods for the coupled nonlinear Schrödinger-KdV equations ⋮ A variant of the discrete gradient method for the solution of the semilinear wave equation under different boundary conditions ⋮ Line integral solution of Hamiltonian systems with holonomic constraints ⋮ Energy-preserving methods for Poisson systems ⋮ High-order energy-conserving line integral methods for charged particle dynamics ⋮ Multiple invariants conserving Runge-Kutta type methods for Hamiltonian problems ⋮ Efficient implementation of Gauss collocation and Hamiltonian boundary value methods ⋮ A generalized Taylor method of order three for the solution of initial value problems in standard and infinity floating-point arithmetic ⋮ Energy conservation issues in the numerical solution of the semilinear wave equation ⋮ Analysis of energy and quadratic invariant preserving (EQUIP) methods ⋮ Hamiltonian Boundary Value Method for the Nonlinear Schrödinger Equation and the Korteweg-de Vries Equation ⋮ Drift-preserving numerical integrators for stochastic Hamiltonian systems ⋮ Runge-Kutta projection methods with low dispersion and dissipation errors ⋮ A note on the continuous-stage Runge-Kutta(-Nyström) formulation of Hamiltonian boundary value methods (HBVMs) ⋮ Arbitrary-order trigonometric Fourier collocation methods for multi-frequency oscillatory systems ⋮ Line integral solution of differential problems ⋮ Spectrally accurate space-time solution of Hamiltonian PDEs

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