Publications

Preprints

Julian Baumstark and Tobias Jahnke.
Improved error bounds for approximations of high-frequency wave propagation in nonlinear dispersive media.
Preprint, 2024

Reviewed articles in journals

Julian Baumstark, Tobias Jahnke, and Christian Lubich.
Polarized high-frequency wave propagation beyond the nonlinear Schrödinger approximation.
SIAM Journal on Mathematical Analysis, Vol. 56, No. 1, 454-473, 2024.
DOI: 10.1137/22M1504810
Paper, Preprint

Elias Gasmi, Tobias Jahnke, Michael Kirn, and Wolfgang Reichel.
Global continua of solutions to the Lugiato–Lefever model for frequency combs obtained by two-mode pumping.
Z. Angew. Math. Phys. 74, 168, 2023.
DOI: 10.1007/s00033-023-02060-3
Paper, Preprint

Konstantin Zerulla and Tobias Jahnke.
Analysis of a Peaceman–Rachford ADI scheme for Maxwell equations in heterogenous media.
J. Math. Anal. Appl. 527 (1), 127355, 2023.
DOI: 10.1016/j.jmaa.2023.127355
Paper, Preprint

Tobias Jahnke and Michael Kirn.
On numerical methods for the semi-nonrelativistic limit system of the nonlinear Dirac equation.
BIT Numerical Mathematics 63:26, 2023.
DOI: 10.1007/s10543-023-00971-1
Paper, Preprint.

Charles-Edouard Bréhier, David Cohen, and Tobias Jahnke.
Splitting integrators for stochastic Lie-Poisson systems.
Math. Comp. 92, 2167-2216, 2023.
DOI: 10.1090/mcom/3829
Paper, Preprint.

Julian Baumstark and Tobias Jahnke.
Approximation of high-frequency wave propagation in dispersive media.
SIAM Journal on Mathematical Analysis, Vol. 55, No. 2, 1214-1245, 2023.
DOI: 10.1137/22M1474035
Paper, Preprint.

Laura P. Lindner, Tobias Gerach, Tobias Jahnke, Axel Loewe, Daniel Weiss, and Christian Wieners.
Efficient time splitting schemes for the monodomain equation in cardiac electrophysiology.
International Journal for Numerical Methods in Biomedical Engineering, Volume 39, Issue 2, 2022.
DOI: 10.1002/cnm.3666
Paper, Preprint.

Tobias Jahnke and Benny Stein.
A multi-level stochastic collocation method for Schrödinger equations with a random potential.
SIAM/ASA J. Uncertain. Quantif. 10, no. 4, 1753–1780, 2022.
DOI: 10.1137/21M1440517
Paper, Preprint.

Janina Gärtner, Philipp Trocha, Rainer Mandel, Christian Koos, Tobias Jahnke, and Wolfgang Reichel.
Bandwidth and conversion efficiency analysis of dissipative Kerr soliton frequency combs based on bifurcation theory.
Phys. Rev. A 100, 033819, 2019.
DOI: 10.1103/PhysRevA.100.033819
Paper, Preprint

Johannes Eilinghoff, Tobias Jahnke, and Roland Schnaubelt.
Error analysis of an energy preserving ADI splitting scheme for the Maxwell equations.
SIAM J. Numer. Anal., 57(3), 1036–1057, 2019.
DOI: 10.1137/18M1203377
Paper, Preprint

Tobias Jahnke and Marcel Mikl.
Adiabatic exponential midpoint rule for the dispersion-managed nonlinear Schrödinger equation.
IMA Journal of Numerical Analysis 39, 1818–1859, 2019.
DOI: 10.1093/imanum/dry04
Paper, Preprint

Tobias Jahnke and Marcel Mikl.
Adiabatic midpoint rule for the dispersion-managed nonlinear Schrödinger equation.
Numer. Math. 138, No. 4, 975-1009, 2018.
DOI: 10.1007/s00211-017-0926-2
Paper, Preprint

Simone Buchholz, Ludwig Gauckler, Volker Grimm, Marlis Hochbruck and Tobias Jahnke.
Closing the gap between trigonometric integrators and splitting for highly oscillatory differential equations.
IMA J Numer Anal 38(1), 57--74, 2018.
DOI: 10.1093/imanum/drx007
Paper, Preprint

Tobias Jahnke, Marcel Mikl and Roland Schnaubelt.
Strang splitting for a semilinear Schrödinger equation with damping and forcing.
J. Math. Anal. Appl. 455 (2), 1051-1071, 2017.
DOI: 10.1016/j.jmaa.2017.06.004
Paper, Preprint

Marlis Hochbruck, Tobias Jahnke and Roland Schnaubelt.
Convergence of an ADI splitting for Maxwell's equations.
Numerische Mathematik 129 (3), 535-561, 2015.
DOI: 10.1007/s00211-014-0642-0
Paper, Preprint

Andreas Arnold and Tobias Jahnke.
On the approximation of high-dimensional differential equations in the hierarchical Tucker format.
BIT Numer. Math. 54, 305–341, 2014.
DOI: 10.1007/s10543-013-0444-2
Paper, Preprint

Tobias Jahnke and Michael Kreim.
Error bound for piecewise deterministic processes modeling stochastic reaction systems.
SIAM Multiscale Model. Simul., 10(4), 1119–1147, 2012.

Tobias Jahnke.
On reduced models for the chemical master equation.
SIAM Multiscale Model. Simul. 9(4), pp. 1646-1676, 2011

Tobias Jahnke and Derya Altintan.
Efficient simulation of discrete stochastic reaction systems with a splitting method.
BIT, 50(4):797–822, 2010.

Tobias Jahnke and Tudor Udrescu.
Solving chemical master equations by adaptive wavelet compression.
J. Comput. Phys. 229 (16), 5724-5741, 2010.

Tobias Jahnke.
An adaptive wavelet method for the chemical master equation.
SIAM J. Sci. Comput. 31 (6), pp. 4373-4394, 2010.

Christof Schütte and Tobias Jahnke.
Towards effective dynamics in complex systems by Markov kernel approximation.
ESAIM, Math. Model. Numer. Anal. 43, No. 4, 721 (2009).

Tobias Jahnke and Wilhelm Huisinga.
A dynamical low-rank approach to the chemical master equation.
Bulletin of Mathematical Biology, 70(8):2283-2302, 2008.

Wilhelm Huisinga, Peter Deuflhard, Tobias Jahnke, and Michael Wulkow.
Adaptive Discrete Galerkin Methods Applied to the Chemical Master Equation.
SIAM J. Sci. Comput. 30 (6), pp. 2990-3011, 2008.

Philipp Metzner, Evelyn Dittmer, Tobias Jahnke, and Christof Schütte.
Generator estimation methods for discretely observed Markov jump processes.
J. Comp. Phys. 227 (1), pp. 353-375, 2007.

Tobias Jahnke and Wilhelm Huisinga.
Solving the chemical master equation for monomolecular reaction systems analytically.
Journal of Mathematical Biology, 54(1):1--26, 2007.

Katina Lorenz, Tobias Jahnke, and Christian Lubich.
Adiabatic integrators for highly oscillatory second-order linear differential equations with time-
varying eigendecomposition.
BIT, 45(1):91--115, 2005.

Tobias Jahnke.
Long-time-step integrators for almost-adiabatic quantum dynamics.
SIAM J. Sci. Comput., 25(6):2145--2164, 2004.

Tobias Jahnke and Christian Lubich.
Numerical integrators for quantum dynamics close to the adiabatic limit.
Numer. Math., 94(2):289--314, 2003.

Tobias Jahnke and Christian Lubich.
Error bounds for exponential operator splittings.
BIT, 40(4):735--744, 2000.

Reviewed articles in conference proceedings

Julian Baumstark and Tobias Jahnke.
Error bounds for approximations of high-frequency wave propagation in nonlinear dispersive media.
Extended abstract, 16th International Conference on Mathematical and Numerical Aspects of Wave Propagation (WAVES 2024), 30 June -- 5 July 2024, Harnack House, Berlin, Germany.

Tobias Jahnke.
Convergence of piecewise deterministic processes modeling two-scale reaction networks.
Simos, Theodore E. (ed.) et al., Numerical analysis and applied mathematics. International conference on numerical analysis and applied mathematics, Kos, Greece, September 19-25, 2012. Vol. 1. Melville, NY: American Institute of Physics (AIP). AIP Conference Proceedings 1479, 31-34 (2012).

Tudor Udrescu and Tobias Jahnke.
An adaptive method for solving Chemical Master Equations using a sparse wavelet basis.
Simos, Theodore E. (ed.) et al., Numerical analysis and applied mathematics. International conference on numerical analysis and applied mathematics 2009, Rethymno, Crete, Greece, September 18--22, 2009. Vol. 1. Melville, NY: American Institute of Physics (AIP). AIP Conference Proceedings 1168, 489-492 (2009).

Tobias Jahnke.
On hybrid models in stochastic reaction kinetics.
Simos, Theodore E. (ed.) et al., Numerical analysis and applied mathematics. International conference on numerical analysis and applied mathematics 2009, Rethymno, Crete, Greece, September 18--22, 2009. Vol. 2. Melville, NY: American Institute of Physics (AIP). AIP Conference Proceedings 1168, 1540–1543 (2009).

Tobias Jahnke and Steffen Galan.
Solving chemical master equations by an adaptive wavelet method.
In T. E. Simos, G. Psihoyios, and C. Tsitouras, editors, Numerical Analysis and applied mathematics: International Conference on Numerical Analysis and Applied Mathematics 2008. Psalidi, Kos, Greece, 16-20 September 2008, volume 1048 of AIP Conference Proceedings, pages 290-293, 2008.

Miscellaneous

Tobias Jahnke.
Time integration of dispersion-managed nonlinear Schrödinger equations.
In: Marlis Hochbruck, Herbert Koch, Sung-Jin Oh, Alexander Ostermann, editors, Nonlinear Evolution Equations: Analysis and Numerics. Oberwolfach Rep. 16 (2019), no. 1, pp. 305–405.
DOI 10.4171/OWR/2019/5

Tobias Jahnke.
Adiabatic integrators for dispersion-managed nonlinear Schrödinger equations.
In: Erwan Faou, Ernst Hairer, Marlis Hochbruck, Christian Lubich, editors, Geometric Numerical Integration. Oberwolfach Rep. 13 (2016), no. 1, pp. 869–948
DOI 10.4171/OWR/2016/18

Tobias Jahnke and Vikram Sunkara.
Error bound for hybrid models of two-scaled stochastic reaction systems.
In: Stephan Dahlke et al., editors, Extraction of quantifiable Information from complex systems. Lecture notes in computational science and engineering 102. Springer (Berlin), 2014. Pages 303-319.

David Cohen, Tobias Jahnke, Katina Lorenz, and Christian Lubich.
Numerical integrators for highly oscillatory Hamiltonian systems: a review.
In: Alexander Mielke, editor, Analysis, Modeling and Simulation of Multiscale Problems. Springer (Berlin), 2006. Pages 553--576.