Publications

Articles submitted for publication

1.

O. Bokanowski and K. Debrabant
High order finite difference schemes for some nonlinear diffusion equations with an obstacle term
Preprint, 2018, arXiv: 1802.05681 [math.NA]

2.

T. B. J°rgensen, A. Wolniakowski, H. Petersen, K. Debrabant, and N. KrŘger
Robust Optimization with Applications to Design of Context Specific Robot Solutions
Submitted for publication, 2017

Peer-reviewed publications

3.

S. Anmarkrud, K. Debrabant, and A. KvŠrn°
General order conditions for stochastic partitioned Runge-Kutta methods
BIT (Accepted for publication)
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4.

A. A. Arara, K. Debrabant, and A. KvŠrn°
Stochastic B-series and order conditions for exponential integrators
Numerical Mathematics and Advanced Applications, ENUMATH 2017, Lecture Notes in Computational Science and Engineering, Springer, Accepted for publication
arXiv: 1801.02051 [math.NA]

5.

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, Accepted for publication

6.

K. Debrabant and A. KvŠrn°
Cheap arbitrary high order methods for single integrand SDEs
BIT 57, no. 1 (2017), pp. 153–168
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7.

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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8.

T. B. J°rgensen, K. Debrabant, and N. KrŘger
Robust optimizing 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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9.

K. Debrabant, S. Gonzßlez-Pinto, and D. Hernßndez-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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10.

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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11.

K. Debrabant and A. R÷▀ler
On the acceleration of the multilevel Monte Carlo method
J. Appl. Probab. 52, no. 2 (2015), pp. 307–322
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12.

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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13.

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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14.

K. Debrabant and A. KvŠrn°
B-series analysis of iterated Taylor methods
BIT 51, no. 3 (2011), pp. 529–553
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15.

K. Debrabant and A. KvŠrn°
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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16.

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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17.

K. Debrabant and A. KvŠrn°
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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18.

K. Debrabant and A. R÷▀ler
Diagonally drift-implicit Runge-Kutta methods of weak order one and two for It˘ SDEs and stability analysis
Appl. Numer. Math. 59, no. 3-4 (2009), pp. 595–607
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19.

K. Debrabant and A. R÷▀ler
Families of efficient second order Runge-Kutta methods for the weak approximation of It˘ stochastic differential equations
Appl. Numer. Math. 59, no. 3-4 (2009), pp. 582–594
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20.

K. Debrabant and A. KvŠrn°
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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21.

K. Debrabant and A. R÷▀ler
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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22.

K. Debrabant and A. R÷▀ler
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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23.

K. Debrabant and A. R÷▀ler
Continuous weak approximation for stochastic differential equations
J. Comput. Appl. Math. 214, no. 1 (2008), pp. 259–273
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24.

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

25.

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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26.

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

27.

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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28.

K. Debrabant and A. R÷▀ler
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

29.

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. DÝez, C. Tiago, and N. ParÚs, International Center for Numerical Methods in Engineering (CIMNE), Barcelona, Spain, 2013, pp. 187–198
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30.

M. B. Giles, K. Debrabant, and A. R÷▀ler
Numerical analysis of multilevel Monte Carlo path simulation using the Milstein discretization: scalar case
Preprint, 2013, arXiv: 1302.4676 [q-fin.CP]

31.

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

32.

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

Habilitation thesis

33.

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

Dissertation

34.

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

35.

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

36.

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