2 citations · 4 across the 6 of their papers we have counts for
6 papers
Projecting to a Slow Manifold: Singularly Perturbed Systems and Legacy Codes
C. W. Gear, T. J. Kaper, I. G. Kevrekidis +1
The long-term dynamics of many dynamical systems evolve on an attracting, invariant "slow manifold" that can be parameterized by a few observable variables. Yet a simulation using…
From molecular dynamics to coarse self-similar solutions: A simple example using equation-free computation
L. Chen, P. G. Debenedetti, C. W. Gear +1
In the context of the recently developed "equation-free" approach to the computer-assisted analysis of complex systems, we illustrate the computation of coarsely self-similar solut…
Constraint-defined Manifolds: a Legacy Code Approach to Low-dimensional Computation
C. W. Gear, I. G. Kevrekidis
If the dynamics of an evolutionary differential equation system possess a low-dimensional, attracting, slow manifold, there are many advantages to using this manifold to perform co…
Reverse Integration for Computing Stationary Points of Unstable Stiff Systems
C. W. Gear, Ioannis Kevrekidis
Using existing, forward-in-time integration schemes, we demonstrate that it is possible to compute unstable, saddle-type fixed points of stiff systems of ODEs when the stable compe…
Deciding the Nature of the "Coarse Equation" through Microscopic Simulations: the Baby-Bathwater Scheme
Ju Li, Panayotis G. Kevrekidis, C. William Gear +1
Recent developments in multiscale computation allow the solution of ``coarse equations'' for the expected macroscopic behavior of microscopically/stochastically evolving particle d…
Boundary processing for Monte Carlo Simulations in the Gap-Tooth Scheme
C. W. Gear, Ioannis G. Kevrekidis
This note reports on a scheme for interpolating the boundary conditions be- tween non-adjacent modeling regions when the model is based on Monte-Carlo computations of a collection…