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

Kristian Debrabant, Anne Kværnø*, Nicky Cordua Mattsson

*Corresponding author for this work

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Abstract

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.
Original languageEnglish
JournalBIT Numerical Mathematics
Volume62
Pages (from-to)1121–1147
ISSN0006-3835
DOIs
Publication statusPublished - 2022

Keywords

  • Highly oscillatory problems
  • Numerical schemes
  • Quadratic invariants
  • Stochastic Lawson
  • Stochastic oscillators

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