75 citations · 283 across the 17 of their papers we have counts for
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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…
Rooted Tree Analysis for Order Conditions of Stochastic Runge-Kutta Methods for the Weak Approximation of Stochastic Differential Equations
Andreas Rößler
A general class of stochastic Runge-Kutta methods for the weak approximation of Itô and Stratonovich stochastic differential equations with a multi-dimensional Wiener process is in…
Families of efficient second order Runge-Kutta methods for the weak approximation of Itô stochastic differential equations
Kristian Debrabant, Andreas Rößler
Recently, a new class of second order Runge-Kutta methods for Itô stochastic differential equations with a multidimensional Wiener process was introduced by Rößler. In contrast to…
Classification of Stochastic Runge-Kutta Methods for the Weak Approximation of Stochastic Differential Equations
Kristian Debrabant, Andreas Rößler
In the present paper, a class of stochastic Runge-Kutta methods containing the second order stochastic Runge-Kutta scheme due to E. Platen for the weak approximation of Itô stochas…
Continuous Weak Approximation for Stochastic Differential Equations
Kristian Debrabant, Andreas Rößler
A convergence theorem for the continuous weak approximation of the solution of stochastic differential equations by general one step methods is proved, which is an extension of a t…
Diagonally drift-implicit Runge-Kutta methods of weak order one and two for Itô SDEs and stability analysis
Kristian Debrabant, Andreas Rößler
The class of stochastic Runge-Kutta methods for stochastic differential equations due to Rößler is considered. Coefficient families of diagonally drift-implicit stochastic Runge-Ku…