Forschung
Participation in funded research projects
| 09/2025 - 11/2025 | Modeling and numerical simulation of pandemic processes in Ghana using a modified Patankar–Runge–Kutta methods Role: Co-writing the proposal and co-collaborator |
| 07/2021 - 06/2024 | Significant expansion and unification of the theory of Patankar-type methods through uniform order analysis, first-time investigation of stability, time step adaptation, and dense output formulae Role: Co-writing the proposal and main investigator of the research |
Supervision
| 02/2023 - today | Co-supervising 1 Ph.D. student, Kassel |
| 08/2022 - 03/2023 | Mentored 1 Master’s student, Kassel |
Other experience of relevance
| 02/2023 - today | Co-supervising 1 Ph.D. student, Kassel |
| 12/2023 - 06/2025 | Reviewer for international Journals: SIAM J. Sci. Comput., J. Comput. Sci., J. Comput. Appl. Math., Appl. Numer. Math. |
| 08/2022 - 03/2023 | Mentored 1 Master’s student, Kassel |
Publications
Peer reviewed in international journals
| 11. A Boot-Strapping Technique to Design Unconditionally Positive Dense Output Formulae for Modified Patankar-Runge-Kutta Methods Communications on Applied Mathematics and Computation (2025). [DOI] |
| 10. Order conditions for Runge-Kutta-like methods with solution-dependent coefficients (with D. Ketcheson, A. Meister) Communications in Applied Mathematics and Computational Science, 20 (1), (2025), 29–66. [DOI] |
| 9. On the non-global linear stability and spurious fixed points of MPRK schemes with negative RK parameters (with S. Kopecz, A. Meister, A. Schilling) Numerical Algorithms, 96, (2024), 1221–1242. [DOI] |
| 8. A necessary condition for non-oscillatory and positivity preserving time-integration schemes (with D. Torlo, P. Öffner) In: Hyperbolic Problems: Theory, Numerics, Applications. Volume II, SEMA SIMAI Springer Ser., Vol. 35, Springer, Cham (2024), 121–131. [DOI] |
| 7. On the local dynamics of first and second order GeCo and gBBKS schemes (with S. Kopecz, A. Martiradonna, A. Meister) Applied Numerical Mathematics, 193, (2023), 43–66. [DOI] |
| 6. A study of the local dynamics of modified Patankar DeC and higher order modified Patankar–RK methods (with P. Öffner) ESAIM: M2AN, 57, (2023), 2319–2348. [DOI] |
| 5. On the Stability of Strong–Stability–Preserving modified Patankar–Runge–Kutta schemes (with J. Huang, S. Kopecz, A. Meister, C.-W. Shu) ESAIM: M2AN, 57, (2023), 1063–1086. [DOI] |
| 4. On the Stability of Unconditionally Positive and Linear Invariants Preserving Time Integration Schemes (with S. Kopecz, A. Meister) SIAM Journal on Numerical Analysis, 60 (6), (2022), 3029–3051. [DOI] |
| 3. On Lyapunov stability of positive and conservative time integrators and application to second order modified Patankar–Runge–Kutta schemes (with S. Kopecz, A. Meister) ESAIM: M2AN, 56 (3), (2022), 1053–1080. [DOI] |
| 2. An Involutive GVW Algorithm and the Computation of Pommaret Bases (with A. Hashemi, D. Robertz, W. M. Seiler) Mathematics in Computer Science, 15, (2021), 419–452. [DOI] |
| 1. Numerical Investigation of Ultrashort Laser-Ablative Synthesis of Metal Nanoparticles in Liquids Using the Atomistic-Continuum Model (with D. S. Ivanov, A. N. Maiorov, V. P. Veiko, B. Rethfeld, Y. I. Dombrovska, A. V. Kabashin) Molecules, 25 (1), (2020), 67–78. [DOI] |
Peer reviewed Conference Proceedings
| 2. A Stability Analysis of Modified Patankar-Runge-Kutta methods for a nonlinear Production-Destruction System (with S. Kopecz, A. Meister) PAMM, 22: e202200083 (2023) [DOI] |
| 1. Recent Developments in the Field of Modified Patankar–Runge–Kutta methods (with S. Kopecz, A. Meister) PAMM, 21: e202100027 (2021) [DOI] |
Thesis
| A Unifying Theory for Runge-Kutta-like Time Integrators: Convergence and Stability PhD Thesis, University of Kassel, KOBRA (2024). [DOI] |