A multiscale method for highly oscillatory dynamical systems using a Poincaré map type technique
type: Item
instance of: scholarly article
title: A multiscale method for highly oscillatory dynamical systems using a Poincaré map type technique
zbMATH Open document ID: 1263.65067
author: Björn Engquist
author: Gil Ariel
author: Seong Jun Kim
author: Yoonsang Lee
author: Richard Tsai
published in: Journal of Scientific Computing
publication date: 2013-04-08T00:00:00Z
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 65P10
zbMATH DE Number: 6151370
zbMATH Keywords: oscillatory dynamical system
zbMATH Keywords: averaging
zbMATH Keywords: multiscale method
zbMATH Keywords: nonstandard splitting
zbMATH Keywords: filtering
zbMATH Keywords: numerical examples
MaRDI profile type: Publication
full work available at URL: s10915-012-9656-x
OpenAlex ID: W2049368507
cites work: Accelerated Simulation of a Heavy Particle in a Gas of Elastic Spheres
cites work: Numerical Multiscale Methods for Coupled Oscillators
cites work: Multiscale Computations for Highly Oscillatory Problems
cites work: A multiscale method for highly oscillatory ordinary differential equations with resonance
cites work: A reversible multiscale integration method
cites work: Oscillatory Systems with Three Separated Time Scales: Analysis and Computation
cites work: A Multiscale Technique for Finding Slow Manifolds of Stiff Mechanical Systems
cites work: Slow observables of singularly perturbed differential equations
cites work: Young Measure Approach to Computing Slowly Advancing Fast Oscillations
cites work: On metastability in FPU
cites work: Resonance, Metastability and Blow up in FPU
cites work: Molecular dynamics and the accuracy of numerically computed averages
cites work: A multiscale method coupling network and continuum models in porous media. I: Steady-state single phase flow
cites work: Numerical Integrators for Highly Oscillatory Hamiltonian Systems: A Review
cites work: On second-order differential equations with highly oscillatory forcing terms
cites work: A study of extrapolation methods based on multistep schemes without parasitic solutions
cites work: Analysis of the heterogeneous multiscale method for ordinary differential equations
cites work: The heterogeneous multiscale methods
cites work: Numerical techniques for multi-scale dynamical systems with stochastic effects
cites work: Q3538693
cites work: Heterogeneous multiscale methods for stiff ordinary differential equations
cites work: Multi-scale methods for wave propagation in heterogeneous media
cites work: A computational strategy for multiscale systems with applications to Lorenz 96 model
cites work: Long-Time-Step Methods for Oscillatory Differential Equations
cites work: Projective Methods for Stiff Differential Equations: Problems with Gaps in Their Eigenvalue Spectrum
cites work: Constraint-defined manifolds: a legacy code approach to low-dimensional computation
cites work: On the energy distribution in Fermi-Pasta-Ulam lattices
cites work: Q4531870
cites work: Exponential integrators
cites work: Q4550964
cites work: Perturbation methods in applied mathematics
cites work: Multiple scale and singular perturbation methods
cites work: Problems with Different Time Scales for Ordinary Differential Equations
cites work: Q4016504
cites work: Q4291772
cites work: Simulating Hamiltonian Dynamics
cites work: Discrete mechanics and variational integrators
cites work: Q4356577
cites work: Averaging methods in nonlinear dynamical systems
cites work: Q4315882
cites work: Nonintrusive and Structure Preserving Multiscale Integration of Stiff ODEs, SDEs, and Hamiltonian Systems with Hidden Slow Dynamics via Flow Averaging
DOI: 10.1007/S10915-012-9656-X
Recommended article: Parareal multiscale methods for highly oscillatory dynamical systems
Recommended article: Q3102059
Recommended article: A multiscale method for highly oscillatory ordinary differential equations with resonance
Recommended article: Variable step size multiscale methods for stiff and highly oscillatory dynamical systems
Recommended article: An accelerated Poincaré-map method for autonomous oscillators
Recommended article: A multiscale computation for highly oscillatory dynamical systems using empirical mode decomposition (EMD)-type methods
Recommended article: Numerical Multiscale Methods for Coupled Oscillators
Recommended article: Multiscale Computations for Highly Oscillatory Problems
Recommended article: An Alternative Perturbation Procedure of Multiple Scales for Nonlinear Dynamics Systems
Recommended article: A perturbation-incremental method for strongly nonlinear autonomous oscillators with many degrees of freedom
description: scientific article; zbMATH DE number 6151370