NUMERICAL TECHNIQUES FOR MULTI-SCALE DYNAMICAL SYSTEMS WITH STOCHASTIC EFFECTS ⁄

By Eric Vanden-Eijnden. 2003

204 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/3771bab99b63d36d9929ab622259cc51bfe12b71

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

1. Björn Engquist
2. E. Weinan
3. Assyr Abdulle
4. Eric Vanden-Eijnden
5. Xiantao Li
6. Weiqing Ren
7. Andrew J. Majda
8. Di Liu

In Computational Theory and Mathematics

1. Björn Engquist
2. Ronald R. Coifman
3. Stéphane Lafon
4. Andrew J. Majda
5. E. Weinan
6. Eric Vanden-Eijnden
7. Assyr Abdulle
8. Ioannis G. Kevrekidis

In Numerical Analysis

1. E. Weinan
2. Björn Engquist
3. Andrew J. Majda
4. Di Liu
5. Assyr Abdulle
6. Ioannis G. Kevrekidis
7. Weiqing Ren
8. Xiantao Li

Citations in the corpus

• Diffusion Maps, Reduction Coordinates, and Low Dimensional Representation of Stochastic Systems (2008, background): “In some situations, the decomposition into slow reduction coordinates and remaining fast variables is assumed known a-priori and/or given explicitly by the forms of the equations, see for example [24, 51, 28].”
• Challenges in Climate Science and Contemporary Applied Mathematics (2012, background): “A key difference between SP and HMM lies in that while reduced HMM time-steppers have been analyzed and applied for various physical systems with wide scale separation, = 10 −3 , 10 −4 , with the scale separation ratio between large and small scales, and rapid local statistical equilibration in time”
• The heterogeneous multiscale method* (2012, methodology): “(3.32) Such systems are widely studied in the construction of multiscale methods; see, for instance, Vanden-Eijnden (2003) or E (2003).”
• Diffusion approximation for fully coupled stochastic differential equations (2020, unknown): “[20, 35, 51, 55] and the references therein.”
• Strong convergence of projective integration schemes for singularly perturbed stochastic differential systems (2006, background): “For the case where y²t satisfies an Itô stochastic equation Kifer [11] proves convergence in the sup-norm and E et al. [12] derive estimates on the rate of strong (L1) convergence to the solution of an effective ordinary differential system (see also Vanden Eijnden [13]).”
• Heterogeneous Multiscale Methods: A Review (2007, methodology): “an HMM type of strategy was independently proposed in [173].”
• Analysis of multiscale methods for stochastic differential equations (2005, methodology): “The basic idea proposed in [25] is to solve (2.”