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math.NA2025
A Class of Stochastic Runge-Kutta Methods for Stochastic Differential Equations Converging with Order 1 in -Norm
Andreas Rößler
For the approximation of solutions for Itô and Stratonovich stochastic differential equations (SDEs)a new class of efficient stochastic Runge-Kutta (SRK) methods is developed. As t…
math.NA2024
An Exponential Stochastic Runge-Kutta Type Method of Order up to 1.5 for SPDEs of Nemytskii-type
Claudine von Hallern, Ricarda Mißfeldt, Andreas Rößler
For the approximation of solutions for stochastic partial differential equations, numerical methods that obtain a high order of convergence and at the same time involve reasonable…
math.NA2020
High order numerical integrators for single integrand Stratonovich SDEs
David Cohen, Kristian Debrabant, Andreas Rößler
We show that applying any deterministic B-series method of order with a random step size to single integrand SDEs gives a numerical method converging in the mean-square and w…