Publications

Articles submitted for publication

1.

K. Debrabant, A. Kværnø, and N. C. Mattsson
Lawson schemes for highly oscillatory stochastic differential equations and conservation of invariants
Preprint, 2019, download arXiv version

2.

K. Debrabant, A. Kværnø, and N. C. Mattsson
Runge–Kutta Lawson schemes for stochastic differential equations
Preprint, 2019, download arXiv version

3.

O. Bokanowski and K. Debrabant
High order finite difference schemes for some nonlinear diffusion equations with an obstacle term
Preprint, 2018, download arXiv version

4.

K. Debrabant, G. Samaey, and P. Zieliński
Study of micro-macro acceleration schemes for linear slow-fast stochastic differential equations with additive noise
Preprint, 2018, download arXiv version

Peer-reviewed publications

5.

A. A. Arara, K. Debrabant, and A. Kværnø
Stochastic B-series and order conditions for exponential integrators
Numerical Mathematics and Advanced Applications, ENUMATH 2017, Lecture Notes in Computational Science and Engineering, Springer, 2019, pp. 419–427
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6.

K. Debrabant, A. Ghasemifard, and N. C. Mattsson
Weak Antithetic MLMC Estimation of SDEs with the Milstein scheme for Low-Dimensional Wiener Processes
Appl. Math. Lett. 91 (2019), pp. 22–27
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7.

M. B. Giles, K. Debrabant, and A. Rößler
Analysis of multilevel Monte Carlo using the Milstein discretisation
Discrete and Continuous Dynamical Systems - Series B 24, no. 8 (2019), pp. 3881–3903
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8.

R. Zimmermann and K. Debrabant
Parametric model reduction via interpolating orthonormal bases
Numerical Mathematics and Advanced Applications, ENUMATH 2017, Lecture Notes in Computational Science and Engineering, Springer, 2019, pp. 683–691
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9.

S. Anmarkrud, K. Debrabant, and A. Kværnø
General order conditions for stochastic partitioned Runge-Kutta methods
BIT 58, no. 2 (2018), pp. 257–280
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10.

T. B. Jørgensen, A. Wolniakowski, H. G. Petersen, K. Debrabant, and N. Krüger
Robust optimization with applications to design of context specific robot solutions
Robotics and Computer-Integrated Manufacturing 53 (2018), pp. 162 –177
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11.

E. Kristensen, H. Røy, K. Debrabant, and T. Valdemarsen
Carbon oxidation and bioirrigation in sediments along a Skagerrak-Kattegat-Belt sea depth transect
Marine Ecology Progress Series (MEPS) 604 (2018), pp. 33–50
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12.

K. Debrabant and A. Kværnø
Cheap arbitrary high order methods for single integrand SDEs
BIT 57, no. 1 (2017), pp. 153–168
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13.

K. Debrabant, G. Samaey, and P. Zieliński
A micro-macro acceleration method for the Monte Carlo simulation of stochastic differential equations
SIAM J. Numer. Anal. 55, no. 6 (2017), pp. 2745–2786
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14.

T. B. Jørgensen, K. Debrabant, and N. Krüger
Robust optimization of robotic pick and place operations for deformable objects through simulation
Proceedings of the 2016 IEEE International Conference on Robotics and Automation, May 16-21, 2016, Stockholm, Sweden, 2016, pp. 3863–3870
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15.

K. Debrabant, S. González-Pinto, and D. Hernández-Abreu
On the global error of special Runge–Kutta methods applied to linear Differential Algebraic Equations
Appl. Math. Lett. 39 (2015), pp. 53–59
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16.

K. Debrabant and J. Lang
On asymptotic global error estimation and control of finite difference solutions for semilinear parabolic equations
Comput. Methods Appl. Mech. Engrg. 288 (2015), pp. 110–126
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17.

K. Debrabant and A. Rößler
On the acceleration of the multilevel Monte Carlo method
J. Appl. Probab. 52, no. 2 (2015), pp. 307–322
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18.

K. Debrabant and E. R. Jakobsen
Semi-Lagrangian schemes for linear and fully non-linear Hamilton-Jacobi-Bellman equations
Hyperbolic Problems: Theory, Numerics, Applications, Proceedings of the Fourteenth International Conference on Hyperbolic Problems held in Padova, June 25-29, 2012, ed. by F. Ancona, A. Bressan, P. Marcati, and A. Marson, vol. 8, AIMS Series on Applied Mathematics, American Institute of Mathematical Sciences (AIMS), Springfield, MO, 2014, pp. 483–490
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19.

K. Debrabant and E. R. Jakobsen
Semi-Lagrangian schemes for linear and fully non-linear diffusion equations
Math. Comp. 82, no. 283 (2013), pp. 1433–1462
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20.

K. Debrabant and A. Kværnø
B-series analysis of iterated Taylor methods
BIT 51, no. 3 (2011), pp. 529–553
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21.

K. Debrabant and A. Kværnø
Composition of stochastic B-series with applications to implicit Taylor methods
Appl. Numer. Math. 61, no. 4 (2011), pp. 501–511
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22.

K. Debrabant
Runge-Kutta methods for third order weak approximation of SDEs with multidimensional additive noise
BIT 50, no. 3 (2010), pp. 541–558
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23.

K. Debrabant and A. Kværnø
Stochastic Taylor expansions: Weight functions of B-series expressed as multiple integrals
Stoch. Anal. Appl. 28, no. 2 (2010), pp. 293–302
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24.

K. Debrabant and A. Rößler
Diagonally drift-implicit Runge-Kutta methods of weak order one and two for Itô SDEs and stability analysis
Appl. Numer. Math. 59, no. 3-4 (2009), pp. 595–607
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25.

K. Debrabant and A. Rößler
Families of efficient second order Runge-Kutta methods for the weak approximation of Itô stochastic differential equations
Appl. Numer. Math. 59, no. 3-4 (2009), pp. 582–594
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26.

K. Debrabant and A. Kværnø
B-series analysis of stochastic Runge-Kutta methods that use an iterative scheme to compute their internal stage values
SIAM J. Numer. Anal. 47, no. 1 (2008/09), pp. 181–203
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27.

K. Debrabant and A. Rößler
Classification of stochastic Runge-Kutta methods for the weak approximation of stochastic differential equations
Math. Comput. Simulation 77, no. 4 (2008), pp. 408–420
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28.

K. Debrabant and A. Rößler
Continuous Runge-Kutta methods for Stratonovich stochastic differential equations
Monte Carlo and quasi-Monte Carlo methods 2006, Berlin: Springer, 2008, pp. 237–250
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29.

K. Debrabant and A. Rößler
Continuous weak approximation for stochastic differential equations
J. Comput. Appl. Math. 214, no. 1 (2008), pp. 259–273
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30.

A. Szentpétery, K. Debrabant, and R. Riquier
Der mathematisch simulierte virtuelle Artikulator und seine Anwendung zur Korrektur virtueller Kauflächen
Quintessenz Zahntechnik 34, no. 2 (2008), pp. 152–160

31.

K. Debrabant and K. Strehmel
Convergence of Runge-Kutta methods applied to linear partial differential-algebraic equations
Appl. Numer. Math. 53, no. 2-4 (2005), pp. 213–229
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32.

W. Lucht and K. Debrabant
On quasi-linear PDAEs with convection: applications, indices, numerical solution
Appl. Numer. Math. 42, no. 1-3 (2002), pp. 297–314
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Book chapters

33.

K. Debrabant and E. R. Jakobsen
Semi-Lagrangian schemes for parabolic equations
Recent developments in computational finance, Foundations, algorithms and applications, ed. by T. Gerstner and P. Kloeden, vol. 14, Interdisciplinary Mathematical Sciences, World Scientific, 2013, chap. 6, pp. 279–298
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34.

K. Debrabant and A. Rößler
Derivative-free weak approximation methods for stochastic differential equations in finance
Recent developments in computational finance, Foundations, algorithms and applications, ed. by T. Gerstner and P. Kloeden, vol. 14, Interdisciplinary Mathematical Sciences, World Scientific, 2013, chap. 7, pp. 299–316
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Further publications

35.

K. Debrabant and J. Lang
On global error estimation and control of finite difference solutions for parabolic equations
Adaptive Modeling and Simulation 2013, ed. by J. P. Moitinho de Almeida, P. Díez, C. Tiago, and N. Parés, International Center for Numerical Methods in Engineering (CIMNE), Barcelona, Spain, 2013, pp. 187–198
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36.

J. Lang, K. Debrabant, and J. Verwer
On global error control for parabolic PDEs
Oberwolfach reports 4 (2007), pp. 1702–1704

37.

K. Debrabant and M. Kiehl
Statik eines Flachdaches
Mathematische Modellierung mit Schülern, Bensheim: Zentrum für Mathematik (2004)

Habilitation thesis

38.

K. Debrabant
Consistency analysis of stochastic Runge-Kutta and Taylor methods
Habilitation thesis, Technische Universität Darmstadt, 2010

Dissertation

39.

K. Debrabant
Numerische Behandlung linearer und semilinearer partieller differentiell-algebraischer Systeme mit Runge-Kutta-Methoden
Dissertation, Martin Luther University Halle-Wittenberg, Oct. 2004

Diploma theses

40.

K. Debrabant
Stringkompaktifizierung mit Termen höherer Ordnung
Diploma thesis, Martin Luther University Halle-Wittenberg, 2001

41.

K. Debrabant
Theoretische und numerische Untersuchungen zu partiellen differentiell-algebraischen Systemen
Diploma thesis, Martin Luther University Halle-Wittenberg, 2000