Numerical Investigation of Ultrashort Laser-Ablative Synthesis of Metal Nanoparticles in Liquids Using the Atomistic-Continuum Model
D. S. Ivanov, T. Izgin, A. N. Maiorov, V. P. Veiko, B. Rethfeld, Y. I. Dombrovska, M. E. Garcia, I. N. Zavestovskaya, S. M. Klimentov, A. V. Kabashin, Molecules 25.1 (2020): 67., PDF
An Involutive GVW Algorithm and the Computation of Pommaret Bases
A. Hashemi, T. Izgin, D. Robertz, W. M. Seiler, Math. Comput. Sci., PDF
Recent Developments in the Field of Modified Patankar-Runge-Kutta-methods
T. Izgin, S. Kopecz, A. Meister, Proceedings in Applied Mathematics & Mechanics (2021), PDF
On Lyapunov stability of positive and conservative time integrators and application to second order modified Patankar-Runge-Kutta schemes
T. Izgin, S. Kopecz, A. Meister, ESAIM: M2AN 56 (3) 1053-1080 (2022), PDF
On the Stability of Unconditionally Positive and Linear Invariants Preserving Time Integration Schemes
T. Izgin, S. Kopecz, A. Meister, SIAM Journal on Numerical Analysis 60 (6) (2022) 3029-3051: PDF
On the stability of strong-stability-preserving modified Patankar-Runge-Kutta schemes
J. Huang, T. Izgin, S. Kopecz, A. Meister, C.-W. Shu, ESAIM: M2AN, 57 2 (2023) 1063-1086: PDF
On the dynamics of first and second order GeCo and gBBKS schemes
T. Izgin, S. Kopecz, A. Martiradonna, A. Meister, Applied
Numerical Mathematics, 193:43-66 (2023): PDF
A stability analysis of modified Patankar--Runge--Kutta methods for a nonlinear production-destruction system
T. Izgin, S. Kopecz, A. Meister, Proc. Appl. Math. Mech., 22: e202200083 (2023): PDF
A study of the local dynamics of modified Patankar DeC and higher order modified Patankar--RK methods
T. Izgin, P. Öffner, ESAIM: Mathematical Modelling and Numerical Analysis, 2023, No 4, p. 2319-2348: PDF
On the non-global linear stability and spurious fixed points of MPRK schemes with negative RK parameters
T. Izgin, S. Kopecz, A. Meister, A. Schilling, Numer. Algor. (2024): PDF
A Unifying Theory for Runge-Kutta-like Time Integrators: Convergence and Stability
T. Izgin, PhD Thesis, University of Kassel, KOBRA (2024): PDF
Submitted
Using Bayesian Optimization to Design Time Step Size Controllers with Application to Modified Patankar--Runge--Kutta Methods
T. Izgin, H. Ranocha, arXiv (2023): PDF
Order conditions for Runge--Kutta-like methods with solution-dependent coefficients
T. Izgin, D. I. Ketcheson, A. Meister, arXiv (2024): PDF
Accepted for publication
A neccesssary condition for non oscillatory and positivity preserving time-integration schemes
T. Izgin, P. Öffner, D. Torlo arXiv (2022): PDF
