Publications

Peer-reviewed publications

1.

A. A. Arara, K. Debrabant, and A. Kværnø
B-series for SDEs with application to exponential integrators for non-autonomous semi-linear problems
Journal of Computational Dynamics (Accepted for publication)
download arXiv version download from publisher

2.

M. Kamrani, K. Debrabant, and N. Jamshidi
Exponential Euler method for stiff stochastic differential equations with additive fractional Brownian noise
International Journal of Computer Mathematics 101, no. 3 (2024), 357 – 371
download arXiv version download from publisher

3.

A. Rathinasamy, K. Debrabant, and P. Nair
Weak convergence of balanced stochastic Runge–Kutta methods for stochastic differential equations
Research in Mathematics 10, no. 1 (2023), ed. by A. Rasila, p. 2163546
free download from publisher

4.

P. B. Christensen, B. Debrabant, S. Cowan, K. Debrabant, A. Øvrehus, and A.-S. Duberg
Hepatitis C time trends in reported cases and estimates of the hidden population born prior to 1965, Denmark and Sweden, 1990 to 2020
Eurosurveillance 27, no. 50 (2022)
free download from publisher

5.

K. Debrabant, A. Kværnø, and N. C. Mattsson
Lawson schemes for highly oscillatory stochastic differential equations and conservation of invariants
BIT 62 (2022), pp. 1121–1147
free download from publisher

6.

O. Bokanowski and K. Debrabant
Backward differentiation formula finite difference schemes for diffusion equations with an obstacle term
IMA J. Numer. Anal. 41, no. 2 (2021), pp. 900–934
download arXiv version download from publisher

7.

K. Debrabant, L. Grønbæk, and C. Kronborg
The cost-effectiveness of a COVID-19 vaccine in a Danish context
Clinical Drug Investigation 41 (2021), pp. 975–988
free view-only version from publisher download from publisher

8.

K. Debrabant, A. Kværnø, and N. C. Mattsson
Runge–Kutta Lawson schemes for stochastic differential equations
BIT 61, no. 2 (2021), pp. 381–409
download arXiv version free view-only version from publisher download from publisher

9.

D. Cohen, K. Debrabant, and A. Rößler
High order numerical integrators for single integrand Stratonovich SDEs
Appl. Numer. Math. 158 (2020), pp. 264–270
free download from publisher

10.

K. Debrabant, G. Samaey, and P. Zieliński
Study of micro-macro acceleration schemes for linear slow-fast stochastic differential equations with additive noise
BIT 60, no. 4 (2020), pp. 959–998
download arXiv version free view-only version from publisher download from publisher

11.

A. A. Arara, K. Debrabant, and A. Kværnø
Stochastic B-series and order conditions for exponential integrators
Numerical Mathematics and Advanced Applications, ENUMATH 2017, vol. 126, Lecture Notes in Computational Science and Engineering, Springer, 2019, pp. 419–427
download arXiv version download from publisher

12.

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
download arXiv version download from publisher

13.

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
download arXiv version download from publisher

14.

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
download from publisher

15.

S. Anmarkrud, K. Debrabant, and A. Kværnø
General order conditions for stochastic partitioned Runge-Kutta methods
BIT 58, no. 2 (2018), pp. 257–280
download arXiv version free view-only version from publisher download from publisher

16.

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
download from publisher

17.

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
free download from publisher

18.

K. Debrabant and A. Kværnø
Cheap arbitrary high order methods for single integrand SDEs
BIT 57, no. 1 (2017), pp. 153–168
download arXiv version free view-only version from publisher download from publisher

19.

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
free download

20.

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
download from publisher

21.

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
download from publisher

22.

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
download arXiv version download from publisher

23.

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

24.

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
free download from publisher

25.

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
download arXiv version download from publisher

26.

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

27.

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
download arXiv version download from publisher

28.

K. Debrabant
Runge-Kutta methods for third order weak approximation of SDEs with multidimensional additive noise
BIT 50, no. 3 (2010), pp. 541–558
download arXiv version free view-only version from publisher download from publisher

29.

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
download from publisher

30.

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
download arXiv version download from publisher

31.

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
download arXiv version download from publisher

32.

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
free download

33.

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
download arXiv version download from publisher

34.

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
download from publisher

35.

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

36.

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

37.

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
download arXiv version download from publisher

38.

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
download arXiv version download from publisher

Book chapters

39.

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
download from publisher

40.

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
download from publisher

Further publications

41.

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
free download from publisher

42.

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

43.

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

Habilitation thesis

44.

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

Dissertation

45.

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

46.

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

47.

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