Publikationsliste

Time integration of highly oscillatory nonlinear Dirac equations. PhD dissertation
Kirn, M.
2025, October 1. Karlsruher Institut für Technologie (KIT). doi:10.5445/IR/1000185176  

Employing nonresonant step sizes for time integration of highly oscillatory nonlinear Dirac equations
Jahnke, T.; Kirn, M.
2024. Karlsruher Institut für Technologie (KIT). doi:10.5445/IR/1000175882  

Analytical and numerical approximations to highly oscillatory solutions of nonlinear Friedrichs systems
Jahnke, T.; Mödl, J.
2024. Karlsruher Institut für Technologie (KIT). doi:10.5445/IR/1000175756  

Improved error bounds for approximations of high-frequency wave propagation in nonlinear dispersive media
Baumstark, J.; Jahnke, T.
2024. Karlsruher Institut für Technologie (KIT). doi:10.5445/IR/1000168785  

Polarized High-frequency Wave Propagation Beyond the Nonlinear Schrödinger Approximation
Baumstark, J.; Jahnke, T.; Lubich, C.
2024. SIAM Journal on Mathematical Analysis, 56 (1), 454–473. doi:10.1137/22M1504810 

Analysis of a Peaceman-Rachford ADI scheme for Maxwell equations in heterogeneous media
Zerulla, K.; Jahnke, T.
2023. Journal of Mathematical Analysis and Applications, 527 (1), Art.-Nr.: 127355. doi:10.1016/j.jmaa.2023.127355 

Splitting integrators for stochastic Lie–Poisson systems
Bréhier, C.-E.; Cohen, D.; Jahnke, T.
2023. Mathematics of Computation, 92 (343), 2167 – 2216. doi:10.1090/mcom/3829 

Global continua of solutions to the Lugiato–Lefever model for frequency combs obtained by two-mode pumping
Gasmi, E.; Jahnke, T.; Kirn, M.; Reichel, W.
2023. Zeitschrift für angewandte Mathematik und Physik, 74 (4), Art.-Nr.: 168. doi:10.1007/s00033-023-02060-3  

On numerical methods for the semi-nonrelativistic limit system of the nonlinear Dirac equation
Jahnke, T.; Kirn, M.
2023. BIT Numerical Mathematics, 63 (2), 26. doi:10.1007/s10543-023-00971-1  

A Fully Parallelized and Budgeted Multi-level Monte Carlo Framework for Partial Differential Equations: From Mathematical Theory to Automated Large-Scale Computations. PhD dissertation
Baumgarten, N.
2023, May 5. Karlsruher Institut für Technologie (KIT). doi:10.5445/IR/1000158415  

Approximation of High-Frequency Wave Propagation in Dispersive Media
Baumstark, J.; Jahnke, T.
2023. SIAM Journal on Mathematical Analysis, 55 (2), 1214–1245. doi:10.1137/22M1474035 

Efficient time splitting schemes for the monodomain equation in cardiac electrophysiology
Lindner, L. P.; Gerach, T.; Jahnke, T.; Loewe, A.; Weiss, D.; Wieners, C.
2023. International Journal for Numerical Methods in Biomedical Engineering, 39 (2), Art.-Nr.: e3666. doi:10.1002/cnm.3666  

A Multilevel Stochastic Collocation Method for Schrödinger Equations with a Random Potential
Jahnke, T.; Stein, B.
2022. SIAM/ASA Journal on Uncertainty Quantification, 10 (4), 1753–1780. doi:10.1137/21M1440517 

Analysis of a Peaceman–Rachford ADI scheme for Maxwell equations in heterogenous media
Zerulla, K.; Jahnke, T.
2022. Karlsruher Institut für Technologie (KIT). doi:10.5445/IR/1000152910  

On numerical methods for the semi-nonrelativistic system of the nonlinear Dirac equation
Jahnke, T.; Kirn, M.
2022. doi:10.5445/IR/1000152783  

Global continua of solutions to the Lugiato–Lefever model for frequency combs obtained by two-mode pumping
Gasmi, E.; Jahnke, T.; Kirn, M.; Reichel, W.
2022. Karlsruher Institut für Technologie (KIT). doi:10.5445/IR/1000151945  

High-frequency wave-propagation: error analysis for analytical and numerical approximations. PhD dissertation
Baumstark, J.
2022, August 24. Karlsruher Institut für Technologie (KIT). doi:10.5445/IR/1000149719  

Efficient time splitting schemes for the monodomain equation in cardiac electrophysiology
Lindner, L. P.; Gerach, T.; Jahnke, T.; Loewe, A.; Weiss, D.; Wieners, C.
2022. Karlsruher Institut für Technologie (KIT). doi:10.5445/IR/1000149976  

Polarized high-frequency wave propagation beyond the nonlinear Schrödinger approximation
Baumstark, J.; Jahnke, T.; Lubich, C.
2022. Karlsruher Institut für Technologie (KIT). doi:10.5445/IR/1000148063  

A multi-level stochastic collocation method for Schrödinger equations with a random potential
Jahnke, T.; Stein, B.
2022. Karlsruher Institut für Technologie (KIT). doi:10.5445/IR/1000143727  

Approximation of high-frequency wave propagation in dispersive media
Baumstark, J.; Jahnke, T.
2022. Karlsruher Institut für Technologie (KIT). doi:10.5445/IR/1000142639  

Approximation of Traveling Waves by Splitting Methods. PhD dissertation
Flohr, R.
2020. Karlsruher Institut für Technologie (KIT). doi:10.5445/IR/1000104725  

Adiabatic exponential midpoint rule for the dispersion-managed nonlinear Schrödinger equation
Jahnke, T.; Mikl, M.
2019. IMA journal of numerical analysis, 39 (4), 1818–1859. doi:10.1093/imanum/dry045 

Bandwidth and conversion efficiency analysis of dissipative Kerr soliton frequency combs based on bifurcation theory
Gärtner, J.; Trocha, P.; Mandel, R.; Koos, C.; Jahnke, T.; Reichel, W.
2019. Physical review / A, 100 (3), 033819. doi:10.1103/PhysRevA.100.033819 

Error analysis of an energy preserving ADI splitting scheme for the Maxwell equations
Eilinghoff, J.; Jahnke, T.; Schnaubelt, R.
2019. SIAM journal on numerical analysis, 57 (3), 1036–1057. doi:10.1137/18M1203377 

Adiabatic midpoint rule for the dispersion-managed nonlinear Schrödinger equation
Jahnke, T.; Mikl, M.
2018. Numerische Mathematik, 138 (4), 975–1009. doi:10.1007/s00211-017-0926-2 

Bandwidth and conversion efficiency analysis of dissipative Kerr soliton frequency combs based on bifurcation theory
Gärtner, J.; Trocha, P.; Mandel, R.; Koos, C.; Jahnke, T.; Reichel, W.
2018. Karlsruher Institut für Technologie (KIT). doi:10.5445/IR/1000089036  

Stochastic Galerkin-collocation splitting for PDEs with random parameters
Jahnke, T.; Stein, B.
2018. Karlsruher Institut für Technologie (KIT). doi:10.5445/IR/1000086905  

Error analysis of an energy preserving ADI splitting scheme for the Maxwell equation
Eilinghoff, J.; Jahnke, T.; Schnaubelt, R.
2018. Karlsruher Institut für Technologie (KIT). doi:10.5445/IR/1000085151  

Closing the gap between trigonometric integrators and splitting methods for highly oscillatory differential equations
Buchholz, S.; Gauckler, L.; Grimm, V.; Hochbruck, M.; Jahnke, T.
2018. IMA journal of numerical analysis, 38 (1), 57–74. doi:10.1093/imanum/drx007 

Time-integration methods for a dispersion-managed nonlinear Schrödinger equation. PhD dissertation
Mikl, M.
2017. Karlsruher Institut für Technologie (KIT). doi:10.5445/IR/1000071577  

Strang splitting for a semilinear Schrödinger equation with damping and forcing
Jahnke, T.; Mikl, M.; Schnaubelt, R.
2017. Journal of mathematical analysis and applications, 455 (2), 1051–1071. doi:10.1016/j.jmaa.2017.06.004 

Adiabatic Midpoint Rule for the dispersion-managed nonlinear Schrödinger Equation
Jahnke, T.; Mikl, M.
2016. Karlsruher Institut für Technologie (KIT). doi:10.5445/IR/1000060572  

Strang splitting for a semilinear Schrödinger equation with damping and forcing
Jahnke, T.; Mikl, M.; Schnaubelt, R.
2016. Karlsruher Institut für Technologie (KIT). doi:10.5445/IR/1000052585  

Analysis and Simulation of Hybrid Models for Reaction Networks. PhD dissertation
Kreim, M.
2014. Karlsruher Institut für Technologie (KIT). doi:10.5445/IR/1000047791  

On the approximation of high-dimensional differential equations in the hierarchical Tucker format
Arnold, A.; Jahnke, T.
2014. BIT - Numerical Mathematics, 54 (2), 305–341. doi:10.1007/s10543-013-0444-2 

Convergence of an ADI splitting for Maxwell’s equations
Hochbruck, M.; Jahnke, T.; Schnaubelt, R.
2014. Numerische Mathematik, 129 (3), 535–561. doi:10.1007/s00211-014-0642-0  

Lösung von hochdimensionalen Anfangswertproblemen durch hierarchische Tensor-Approximation. PhD dissertation
Arnold, A. T.
2013. Karlsruher Institut für Technologie (KIT). doi:10.5445/IR/1000036112  

Convergence of piecewise deterministic processes modeling two-scale reaction networks
Jahnke, T.
2012. 10th International Conference of Numerical Analysis and Applied Mathematics (ICNAAM’12), Kos, Greece, September 19-25, 2012. Ed.: T.E. Simos, 31/1–1, American Institute of Physics (AIP). doi:10.1063/1.4756055 

Error Bound for Piecewise Deterministic Processes Modeling Stochastic Reaction Systems
Jahnke, T.; Kreim, M.
2012. Multiscale Modeling and Simulation, 10 (4), 1119–1147. doi:10.1137/120871894 

On the approximation of high-dimensional differential equations in the hierarchical Tucker format
Arnold, A.; Jahnke, T.
2012. Karlsruher Institut für Technologie (KIT). doi:10.5445/IR/1000029523  

Numerical Methods for the Chemical Master Equation. PhD dissertation
Udrescu, T.
2012. Karlsruher Institut für Technologie (KIT). doi:10.5445/IR/1000029251  

Error bound for piecewise deterministic processes modeling stochastic reaction systems
Jahnke, T.; Kreim, M.
2012. Karlsruher Institut für Technologie (KIT). doi:10.5445/IR/1000028339  

On Reduced Models for the Chemical Master Equation
Jahnke, T.
2011. Multiscale Modeling and Simulation, 9 (4), 1646–1676. doi:10.1137/110821500 

On Reduced Models For The Chemical Master Equation
Jahnke, T.
2011. Karlsruher Institut für Technologie (KIT). doi:10.5445/IR/1000024897  

Efficient simulation of discrete stochastic reaction systems with a splitting method
Jahnke, T.; Altintan, D.
2011. Karlsruher Institut für Technologie (KIT). doi:10.5445/IR/1000024896  

Solving chemical master equations by adaptive wavelet compression
Jahnke, T.; Udrescu, T.
2010. Journal of Computational Physics, 229 (16), 5724–5741. doi:10.1016/j.jcp.2010.04.015 

Efficient simulation of discrete stochastic reaction systems with a splitting method
Jahnke, T.; Altintan, D.
2010. BIT - Numerical Mathematics, 50 (4), 797–822. doi:10.1007/s10543-010-0286-0 

An Adaptive Wavelet Method for the Chemical Master Equation
Jahnke, T.
2010. SIAM Journal on Scientific Computing, 31 (6), 4373–4394. doi:10.1137/080742324 

Solving chemical master equations by adaptive wavelet compression
Jahnke, T.; Udrescu, T.
2010. Karlsruher Institut für Technologie (KIT). doi:10.5445/IR/1000018826  

Towards Effective Dynamics in Complex Systems by Markov Kernel Approximation
Schütte, C.; Jahnke, T.
2010. Karlsruher Institut für Technologie (KIT). doi:10.5445/IR/1000018825  

An Adaptive Wavelet Method for The Chemical Master Equation
Jahnke, T.
2010. Karlsruher Institut für Technologie (KIT). doi:10.5445/IR/1000018824  

On Hybrid Models in Stochastic Reaction Kinetics
Jahnke, T.
2009. 7th International Conference on Numerical Analysis and Applied Mathematics (ICNAAM’09), Rethymno, Greece, September 18-22, 2012. Ed.: T.E. Simos, 1540/1–1, American Institute of Physics (AIP). doi:10.1063/1.3241395 

An Adaptive Method for Solving Chemical Master Equations using a Sparse Wavelet Basis
Jahnke, T.; Udrescu, T.
2009. 7th International Conference on Numerical Analysis and Applied Mathematics (ICNAAM’09), Rethymno, Greece, September 18-22, 2012. Ed.: T.E. Simos, 489/1–1, American Institute of Physics (AIP). doi:10.1063/1.3241504 

Towards effective dynamics in complex systems by Markov kernel approximation
Schütte, C.; Jahnke, T.
2009. Mathematical Modelling and Numerical Analysis, 43 (4), 721–742. doi:10.1051/m2an/2009027 

Solving chemical master equations by an adaptive wavelet method
Jahnke, T.; Galan, S.
2008. Numerical analysis and applied mathematics. International Conference on Numerical Analysis and Applied Mathematics 2008, Psalidi, Kos, Greece, 16 - 20 September 2008. Ed.: G. Simos, 290–293, American Institute of Physics (AIP) 

A dynamical low-rank approach to the chemical master equation
Jahnke, T.; Huisinga, W.; Wulkow, M.
2008. Bulletin of Mathematical Biology, 70 (8), 2283–2302 

Adaptive Discrete Galerkin Methods Applied to the Chemical Master Equation
Huisinga, W.; Deuflhard, P.; Jahnke, T.; Wulkow, M.
2008. SIAM journal on scientific computing, 30 (6), 2990–3011 

Generator estimation methods for discretely observed Markov jump processes
Metzner, P.; Dittmer, E.; Jahnke, T.; Schütte, C.
2007. Journal of Computational Physics, 227 (1), 353–375 

Solving the chemical master equation for monomolecular reaction systems analytically
Jahnke, T.; Huisinga, W.
2007. Journal of Mathematical Biology, 54 (1), 1–26 

Numerical Integrators for Highly Oscillatory Hamiltonian Systems: A Review
Cohen, D.; Jahnke, T.; Lorenz, K.; Lubich, C.
2006. Analysis, Modeling and Simulation of Multiscale Problems. Ed.: A. Mielke, 553–576, Springer-Verlag. doi:10.1007/3-540-35657-6_20 

Adiabatic Integrators for Highly Oscillatory Second-Order Linear Differential Equations with Time-Varying Eigendecomposition
Lorenz, K.; Jahnke, T.; Lubich, C.
2005. BIT - Numerical Mathematics, 45 (1), 91–115. doi:10.1007/s10543-005-2637-9 

Long-Time-Step Integrators for Almost-Adiabatic Quantum Dynamics
Jahnke, T.
2004. SIAM Journal on Scientific Computing, 25 (6), 2145–2164. doi:10.1137/S1064827502411316 

Numerical integrators for quantum dynamics close to the adiabatic limit
Jahnke, T.; Lubich, C.
2003. Numerische Mathematik, 94 (2), 289–314. doi:10.1007/s00211-002-0421-1 

Error Bounds for Exponential Operator Splittings
Jahnke, T.; Lubich, C.
2000. BIT - Numerical Mathematics, 40 (4), 735–744. doi:10.1023/A:1022396519656