Numerical Initial Value Problems in Ordinary Differential Equations
Numerical Initial Value Problems in Ordinary Differential Equations
Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations
Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations
Projective Methods for Stiff Differential Equations: Problems with Gaps in Their Eigenvalue Spectrum
SIAM Journal on Scientific Computing
Telescopic projective methods for parabolic differential equations
Journal of Computational Physics
Quantifying Uncertainty for Non-Gaussian Ensembles in Complex Systems
SIAM Journal on Scientific Computing
A general strategy for designing seamless multiscale methods
Journal of Computational Physics
Approximate linear response for slow variables of dynamics with explicit time scale separation
Journal of Computational Physics
A Multiscale Method for Highly Oscillatory Dynamical Systems Using a Poincaré Map Type Technique
Journal of Scientific Computing
Multiscale stochastic simulations of chemical reactions with regulated scale separation
Journal of Computational Physics
| Hi-index | 31.48 |
Numerical schemes for systems with multiple spatio-temporal scales are investigated. The multiscale schemes use asymptotic results for this type of systems which guarantee the existence of an effective dynamics for some suitably defined modes varying slowly on the largest scales. The multiscale schemes are analyzed in general, then illustrated on a specific example of a moderately large deterministic system displaying chaotic behavior due to Lorenz. Issues like consistency, accuracy, and efficiency are discussed in detail. The role of possible hidden slow variables as well as additional effects arising on the diffusive time-scale are also investigated. As a byproduct we obtain a rather complete characterization of the effective dynamics in Lorenz model.