116 citations · 562 across the 17 of their papers we have counts for
18 papers
Error Bound and Stability Analysis for a Randomized Singly Diagonally Implicit Runge-Kutta Method
Monika Eisenmann, Marvin Jans, Raphael Kruse +1
A randomized Singly Diagonally Implicit Runge-Kutta (SDIRK) method, based on the randomized trapezoidal rule as the underlying quadrature scheme, is proposed. Every realization of…
The BDF2-Maruyama Scheme for Stochastic Evolution Equations with Monotone Drift
Raphael Kruse, Rico Weiske
We study the numerical approximation of stochastic evolution equations with a monotone drift driven by an infinite-dimensional Wiener process. To discretize the equation, we combin…
Application of Randomized Quadrature Formulas to the Finite Element Method for Elliptic Equations
Raphael Kruse, Nick Polydorides, Yue Wu
The implementation of the finite element method for linear elliptic equations requires to assemble the stiffness matrix and the load vector. In general, the entries of this matrix-…
Error estimates of the backward Euler-Maruyama method for multi-valued stochastic differential equations
Monika Eisenmann, Mihály Kovács, Raphael Kruse +1
In this paper, we derive error estimates of the backward Euler-Maruyama method applied to multi-valued stochastic differential equations. An important example of such an equation i…
A randomized and fully discrete Galerkin finite element method for semilinear stochastic evolution equations
Raphael Kruse, Yue Wu
In this paper the numerical solution of non-autonomous semilinear stochastic evolution equations driven by an additive Wiener noise is investigated. We introduce a novel fully disc…
Two quadrature rules for stochastic Itô-integrals with fractional Sobolev regularity
Monika Eisenmann, Raphael Kruse
In this paper we study the numerical quadrature of a stochastic integral, where the temporal regularity of the integrand is measured in the fractional Sobolev-Slobodeckij norm in $…
On a randomized backward Euler method for nonlinear evolution equations with time-irregular coefficients
Monika Eisenmann, Mihály Kovács, Raphael Kruse +1
In this paper we introduce a randomized version of the backward Euler method, that is applicable to stiff ordinary differential equations and nonlinear evolution equations with tim…
A randomized Milstein method for stochastic differential equations with non-differentiable drift coefficients
Raphael Kruse, Yue Wu
In this paper a drift-randomized Milstein method is introduced for the numerical solution of non-autonomous stochastic differential equations with non-differentiable drift coeffici…
Error analysis of randomized Runge-Kutta methods for differential equations with time-irregular coefficients
Raphael Kruse, Yue Wu
This paper contains an error analysis of two randomized explicit Runge-Kutta schemes for ordinary differential equations (ODEs) with time-irregular coefficient functions. In partic…
A discrete stochastic Gronwall Lemma
Raphael Kruse, Michael Scheutzow
We derive a discrete version of the stochastic Gronwall Lemma found in [Scheutzow, IDAQP, 2013]. The proof is based on a corresponding deterministic version of the discrete Gronwal…
Stochastic C-stability and B-consistency of explicit and implicit Milstein-type schemes
Wolf-Jürgen Beyn, Elena Isaak, Raphael Kruse
This paper focuses on two variants of the Milstein scheme, namely the split-step backward Milstein method and a newly proposed projected Milstein scheme, applied to stochastic diff…
Mean-square convergence of the BDF2-Maruyama and backward Euler schemes for SDE satisfying a global monotonicity condition
Adam Andersson, Raphael Kruse
In this paper the numerical approximation of stochastic differential equations satisfying a global monotonicity condition is studied. The strong rate of convergence with respect to…
Stochastic C-stability and B-consistency of explicit and implicit Euler-type schemes
Wolf-Jürgen Beyn, Elena Isaak, Raphael Kruse
This paper is concerned with the numerical approximation of stochastic ordinary differential equations, which satisfy a global monotonicity condition. This condition includes sever…
Duality in refined Sobolev-Malliavin spaces and weak approximations of SPDE
Adam Andersson, Raphael Kruse, Stig Larsson
We introduce a new family of refined Sobolev-Malliavin spaces that capture the integrability in time of the Malliavin derivative. We consider duality in these spaces and derive a B…
Consistency and Stability of a Milstein-Galerkin Finite Element Scheme for Semilinear SPDE
Raphael Kruse
We present an abstract concept for the error analysis of numerical schemes for semilinear stochastic partial differential equations (SPDEs) and demonstrate its usefulness by provin…
Optimal Regularity for Semilinear Stochastic Partial Differential Equations with Multiplicative Noise
Raphael Kruse, Stig Larsson
This paper deals with the spatial and temporal regularity of the unique Hilbert space valued mild solution to a semilinear stochastic partial differential equation with nonlinear t…
Optimal Error Estimates of Galerkin Finite Element Methods for Stochastic Partial Differential Equations with Multiplicative Noise
Raphael Kruse
We consider Galerkin finite element methods for semilinear stochastic partial differential equations (SPDEs) with multiplicative noise and Lipschitz continuous nonlinearities. We a…
An integral method for solving nonlinear eigenvalue problems
Wolf-Jürgen Beyn
We propose a numerical method for computing all eigenvalues (and the corresponding eigenvectors) of a nonlinear holomorphic eigenvalue problem that lie within a given contour in th…