Weak Second Order Multirevolution Composition Methods for Highly Oscillatory Stochastic Differential Equations with Additive or Multiplicative Noise

Vilmart, Gilles

doi:10.1137/130935331

Scientific article

English

Weak Second Order Multirevolution Composition Methods for Highly Oscillatory Stochastic Differential Equations with Additive or Multiplicative Noise

Contributors

Vilmart, Gilles

Published in

SIAM journal on scientific computing, vol. 36, no. 4, p. A1770-A1796

Publication date

2014

Abstract

We introduce a class of numerical methods for highly oscillatory systems of stochastic differential equations with general noncommutative noise. We prove global weak error bounds of order two uniformly with respect to the stiffness of the oscillations, which permits to use large time steps. The approach is based on the micro-macro framework of multi-revolution composition methods recently introduced for deterministic problems and inherits its geometric features, in particular to design integrators preserving exactly quadratic first integral. Numerical experiments, including the stochastic nonlinear Schrödinger equation with space-time multiplicative noise, illustrate the performance and versatility of the approach.

Keywords

Highly-oscillatory stochastic differential equation
Composition method
Quadratic first integral conservation
Multiplicative noise
Time-dependent stochastic
Schrödinger equation

UNIGE affiliation entities

Faculté des sciences / Section de mathématiques

UNIGE research groups

Analyse numérique

Citation (ISO format)

VILMART, Gilles. Weak Second Order Multirevolution Composition Methods for Highly Oscillatory Stochastic Differential Equations with Additive or Multiplicative Noise. In: SIAM journal on scientific computing, 2014, vol. 36, n° 4, p. A1770–A1796. doi: 10.1137/130935331

Article (Published version)

Identifiers

PID : unige:41846
DOI : 10.1137/130935331

Journal ISSN

1064-8275

852views

816downloads

Creation

12/11/2014 15:42:00

First validation

12/11/2014 15:42:00

Update

14/03/2023 22:15:20

Status update

14/03/2023 22:15:20

Last indexation

30/10/2024 20:45:17

Weak Second Order Multirevolution Composition Methods for Highly Oscillatory Stochastic Differential Equations with Additive or Multiplicative Noise

Contributors

Published in

Publication date

Abstract

Keywords

UNIGE affiliation entities

UNIGE research groups

Citation (ISO format)

Main files (1)

Identifiers

Journal ISSN

Technical informations

Creation

First validation

Update

Status update

Last indexation