Enhancing energy conserving methods
type: Item
instance of: scholarly article
title: Enhancing energy conserving methods
zbMATH Open document ID: 0858.65067
DOI: 10.1007/BF01740549
author: Sebastian Reich
published in: BIT
publication date: 1997-04-02T00:00:00Z
review text: This paper is concerned with numerical methods for solving Hamiltonian problems which are energy-conserving. Since some implicit symplectic methods such as the Gauss Runge-Kutta methods suffer form instability due to resonance a new method based on the implicit midpoint rule is constructed. In this formulation, the potential energy function in the Hamiltonian system is split into two -- the strong part is then solved by an energy conserving method and the weak part by an explicit symplectic method such as \textit{L. Verlet}'s method [Computer `experiments' on classical fluids. I. Thermodynamical properties of Lennard-Jones molecules, Phys. Rev. 159, 98-103 (1967)]. The demonstration of the stability of this approach is done numerically.
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 37-XX
Mathematics Subject Classification ID: 65L20
zbMATH DE Number: 881188
zbMATH Keywords: Verlet's method
zbMATH Keywords: implicit symplectic methods
zbMATH Keywords: Gauss Runge-Kutta methods
zbMATH Keywords: instability
zbMATH Keywords: Hamiltonian system
zbMATH Keywords: energy conserving method
zbMATH Keywords: explicit symplectic method
zbMATH Keywords: stability
reviewed by: Kevin Burrage
MaRDI profile type: Publication
cites work: Q3996938
cites work: Dangers of multiple time step methods
cites work: Lie-Poisson Hamilton-Jacobi theory and Lie-Poisson integrators
cites work: Conservative numerical methods for \(\ddot x=f(x)\)
cites work: Q4860575
cites work: Q4860577
cites work: Energy and momentum conserving methods of arbitrary order for the numerical integration of equations of motion. II: Motion of a system of particles
cites work: Lectures on Mechanics
cites work: Momentum conserving symplectic integrators
cites work: Smoothed dynamics of highly oscillatory Hamiltonian systems
cites work: Q4016507
cites work: The discrete energy-momentum method. Conserving algorithms for nonlinear elastodynamics
description: scientific article; zbMATH DE number 881188