Nicky Cordua Mattsson

arXiv2021

Lawson schemes for highly oscillatory stochastic differential equations and conservation of invariants

In this paper, we consider a class of stochastic midpoint and trapezoidal Lawson schemes for the numerical discretization of highly oscillatory stochastic differential equations. These Lawson schemes incorporate both the linear drift and diffusion terms in the exponential operator. We prove that the midpoint Lawson schemes preserve quadratic invariants and discuss this property as well for the trapezoidal Lawson scheme. Numerical experiments demonstrate that the integration error for highly oscillatory problems is smaller than that of some standard methods.

math.NA↗

arXiv2020

Runge-Kutta Lawson schemes for stochastic differential equations

In this paper, we present a framework to construct general stochastic Runge-Kutta Lawson schemes. We prove that the schemes inherit the consistency and convergence properties of the underlying Runge-Kutta scheme, and confirm this in some numerical experiments. We also investigate the stability properties of the methods and show for some examples, that the new schemes have improved stability properties compared to the underlying schemes.

math.NA↗