On the numerical discretisation of stochastic oscillators

作者：Cohen David^*

来源：Mathematics and Computers in Simulation, 2012, 82(8): 1478-1495.

DOI：10.1016/j.matcom.2012.02.004

• Stochastic oscillators
• Highly oscillatory problems
• Kubo oscillator
• Langevin equation
• Numerical schemes
• Stochastic trigonometric integrators

In this article, we propose an approach, based on the variation-of-constants formula, for the numerical discretisation over long-time intervals of several stochastic oscillators. Additive and multiplicative noises are treated separately. The proposed schemes permit the use of large step sizes in the presence of a high frequency in the problem and offer various additional properties. These new numerical integrators can be viewed as a stochastic-generalisation of the trigonometric integrators for highly oscillatory deterministic problems.

• 出版日期2012-4