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Raphael Kruse
,
Nick Polydorides
,
Yue Wu
(2019).
Application of Randomized Quadrature Formulas to the Finite Element Method for Elliptic Equations
.
ArXiv Preprint
.
Preprint
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Raphael Kruse
,
Yue Wu
(2019).
A randomized Milstein method for stochastic differential equations with non-differentiable drift coefficients
.
Discrete & Continuous Dynamical Systems - Ser. B
, vol.
24
(8), 3475-3502.
Preprint
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DOI
Monika Eisenmann
,
Mihály Kovács
,
Raphael Kruse
,
Stig Larsson
(2019).
Error Estimates of the Backward Euler-Maruyama Method for Multi-Valued Stochastic Differential Equations
.
ArXiv Preprint
.
Preprint
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Monika Eisenmann
,
Raphael Kruse
(2019).
Two quadrature rules for stochastic Itô-integrals with fractional Sobolev regularity
.
Communications in Mathematical Sciences
, vol.
16
(8), 2125-2146.
Preprint
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DOI
Raphael Kruse
,
Yue Wu
(2019).
A randomized and fully discrete Galerkin finite element method for semilinear stochastic evolution equations
.
Mathematics of Computation
, vol.
88
, 2793-2825.
Preprint
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DOI
Monika Eisenmann
,
Mihály Kovács
,
Raphael Kruse
,
Stig Larsson
(2019).
On a randomized backward Euler method for nonlinear evolution equations with time-irregular coefficients
.
Foundations of Computational Mathematics
, vol.
19
, 1387-1430.
Preprint
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DOI
Raphael Kruse
,
Michael Scheutzow
(2018).
A discrete stochastic Gronwall lemma
.
Mathematics and Computers in Simulation
, vol.
143
, 149-157.
Preprint
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DOI
Raphael Kruse
,
Yue Wu
(2017).
Error analysis of randomized Runge-Kutta methods for differential equations with time-irregular coefficients
.
Computational Methods in Applied Mathematics
, vol.
17
(3), 479-498.
Preprint
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DOI
Wolf-Jürgen Beyn
,
Elena Isaak
,
Raphael Kruse
(2017).
Stochastic C-stability and B-consistency of explicit and implicit Milstein-type schemes
.
Journal of Scientific Computing
, vol.
70
, 1042-1077.
Preprint
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DOI
Adam Andersson
,
Raphael Kruse
(2017).
Mean-square convergence of the BDF2-Maruyama and backward Euler schemes for SDE satisfying a global monotonicity condition
.
BIT Numerical Mathematics
, vol.
57
, 21-53.
Preprint
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DOI
Wolf-Jürgen Beyn
,
Elena Isaak
,
Raphael Kruse
(2016).
Stochastic C-stability and B-consistency of explicit and implicit Euler-type schemes
.
Journal of Scientific Computing
, vol.
67
, 955-987.
Preprint
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DOI
Adam Andersson
,
Raphael Kruse
,
Stig Larsson
(2016).
Duality in refined Sobolev-Malliavin spaces and weak approximation of SPDE
.
Stochastics and Partial Differential Equations: Analysis and Computations
, vol.
4
, 113-149.
Preprint
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DOI
Raphael Kruse
(2014).
Consistency and stability of a Milstein-Galerkin finite element scheme for semilinear SPDE
.
Stochastic Partial Differential Equations: Analysis and Computations
, vol.
2
, 471-516.
Preprint
PDF
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DOI
Raphael Kruse
(2014).
Strong and Weak Approximation of Semilinear Stochastic Evolution Equations
.
Lecture Notes in Mathematics
, vol.
2093
, Springer, Cham.
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DOI
Raphael Kruse
(2014).
Optimal error estimates of Galerkin finite element methods for stochastic partial differential equations with multiplicative noise
.
IMA Journal of Numerical Analysis
, vol.
34
(1), 217-251.
Preprint
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DOI
Raphael Kruse
,
Stig Larsson
(2012).
Optimal regularity for semilinear stochastic partial differential equations with multiplicative noise
.
Electronic Journal of Probability
, vol.
17
, no. 65, 19 pp.
Preprint
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DOI
Raphael Kruse
(2012).
Characterization of bistability for stochastic multistep methods
.
BIT Numerical Mathematics
, vol.
52
, 109-140.
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DOI
Wolf-Jürgen Beyn
,
Raphael Kruse
(2010).
Two-sided error estimates for the stochastic theta method
.
Discrete & Continuous Dynamical Systems - Ser. B
, vol.
24
(2), 389-407.
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DOI
Raphael Kruse
(2010).
Discrete approximation of stochastic differential equations
.
SeMA Journal
, vol.
51
, 83-90.
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DOI
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