Analysis of the accuracy and convergence of equation-free projection to a slow manifold

DOI10.1051/m2an/2009026zbMath1194.35077arXiv0707.1614OpenAlexW2134118243MaRDI QIDQ5192621

C. William Gear, Antonios Zagaris, Ioannis G. Kevrekidis, Tasso J. Kaper

Publication date: 6 August 2009

Published in: ESAIM: Mathematical Modelling and Numerical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0707.1614

zbMATH Keywords

iterative initializationlegacy codesrecursive projection methoddaesNewton-Krylov generalized minimal residual method

Mathematics Subject Classification ID

Singular perturbations in context of PDEs (35B25) Stability and convergence of numerical methods for ordinary differential equations (65L20) Inertial manifolds (35B42)

Related Items (19)

Exponential estimates of symplectic slow manifolds ⋮ Convergence of Equation-Free Methods in the Case of Finite Time Scale Separation with Application to Deterministic and Stochastic Systems ⋮ Towards Differential Geometric Characterization of Slow Invariant Manifolds in Extended Phase Space: Sectional Curvature and Flow Invariance ⋮ An efficient Newton-Krylov implementation of the constrained runs scheme for initializing on a slow manifold ⋮ Extending the zero-derivative principle for slow-fast dynamical systems ⋮ Two novel families of multiscale staggered patch schemes efficiently simulate large-scale, weakly damped, linear waves ⋮ Data-driven control of agent-based models: an equation/variable-free machine learning approach ⋮ INVITED: Slow manifold reduction for plasma science ⋮ Entropy-related extremum principles for model reduction of dissipative dynamical systems ⋮ Smooth initialization of lattice Boltzmann schemes ⋮ Minimal curvature trajectories: Riemannian geometry concepts for slow manifold computation in chemical kinetics ⋮ Equation-free computation of coarse-grained center manifolds of microscopic simulators ⋮ Lifting in hybrid lattice Boltzmann and PDE models ⋮ On unifying concepts for trajectory-based slow invariant attracting manifold computation in kinetic multiscale models ⋮ Guiding center dynamics as motion on a formal slow manifold in loop space ⋮ Slow Invariant Manifolds of Slow–Fast Dynamical Systems ⋮ Computation of Saddle-Type Slow Manifolds Using Iterative Methods ⋮ On convergence of higher order schemes for the projective integration method for stiff ordinary differential equations ⋮ A numerical method for the approximation of stable and unstable manifolds of microscopic simulators

Uses Software

• KELLEY

Cites Work

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• Analysis of the computational singular perturbation reduction method for chemical kinetics
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• Stabilization of Unstable Procedures: The Recursive Projection Method
• Accuracy of Hybrid Lattice Boltzmann/Finite Difference Schemes for Reaction-Diffusion Systems
• Mesoscale Analysis of the Equation-Free Constrained Runs Initialization Scheme
• Problems with Different Time Scales for Ordinary Differential Equations
• Fast and Slow Dynamics for the Computational Singular Perturbation Method
• Problems with Different Time Scales for Nonlinear Partial Differential Equations
• Projecting to a Slow Manifold: Singularly Perturbed Systems and Legacy Codes

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