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

Gilles Vilmart | Zendy

Open Access

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

Author(s) -

Gilles Vilmart

Publication year - 2014

Publication title -

siam journal on scientific computing

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.674

H-Index - 147

eISSN - 1095-7197

pISSN - 1064-8275

DOI - 10.1137/130935331

Subject(s) - integrator , mathematics , noise (video) , quadratic equation , multiplicative noise , nonlinear system , stochastic differential equation , multiplicative function , computer science , mathematical analysis , physics , image (mathematics) , computer network , geometry , bandwidth (computing) , signal transfer function , digital signal processing , quantum mechanics , artificial intelligence , analog signal , computer hardware

International audienceWe 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

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