18 citations · 44 across the 7 of their papers we have counts for
7 papers · 1 filter
B-series for SDEs with application to exponential integrators for non-autonomous semi-linear problems
Alemayehu Adugna Arara, Kristian Debrabant, Anne Kværnø
In this paper a set of previous general results for the development of B--series for a broad class of stochastic differential equations has been collected. The applicability of the…
Lawson schemes for highly oscillatory stochastic differential equations and conservation of invariants
Kristian Debrabant, Anne Kværnø, Nicky Cordua Mattsson
In this paper, we consider a class of stochastic midpoint and trapezoidal Lawson schemes for the numerical discretization of highly oscillatory stochastic differential equations. T…
Runge-Kutta Lawson schemes for stochastic differential equations
Kristian Debrabant, Anne Kværnø, Nicky Cordua Mattsson
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 th…
Stability Analysis and Classification of Runge-Kutta Methods for Index 1 Stochastic Differential-Algebraic Equations with Scalar Noise
Dominique Küpper, Anne Kværnø, Andreas Rößler
The problem of solving stochastic differential-algebraic equations (SDAEs) of index one with a scalar driving Brownian motion is considered. Recently, the authors proposed a class…
Higher order splitting methods with modified integrators for a class of Hamiltonian systems
Asif Mushtaq, Anne Kværnø, Kåre Olaussen
We discuss systematic extensions of the standard (St{ö}rmer-Verlet) splitting method for differential equations of Hamiltonian mechanics, with relative accuracy of order for…
Stochastic B-series analysis of iterated Taylor methods
Kristian Debrabant, Anne Kværnø
For stochastic implicit Taylor methods that use an iterative scheme to compute their numerical solution, stochastic B--series and corresponding growth functions are constructed. Fr…
Composition of stochastic B-series with applications to implicit Taylor methods
Kristian Debrabant, Anne Kværnø
In this article, we construct a representation formula for stochastic B-series evaluated in a B-series. This formula is used to give for the first time the order conditions of impl…