Research

Research interests

Numerical Analysis, Hyperbolic PDEs and conservation laws
Unconditionally positive and structure-preserving numerical methods
Stability of nonlinear methods
Positivity-preserving Dense Output formulae
Optimal time step control and parameter estimation using ML

Participation in funded research projects

09/2026 - 02/2028	Stable Residual Distribution schemes using Unconditionally Positive methods (STARD-UP) Role: Applicant and PI, DAAD PRIME
01/2026 - 07/2026	Unconditionally Positive Numerical Schemes preserving Entropy Properties via Relaxation Role: Applicant and PI, Fulbright Germany
01/2026 - 07/2026	Unconditionally Positive Numerical Schemes preserving Entropy Properties via Relaxation Role: Applicant and PI, DAAD
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, German Research Foundation
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, German Research Foundation

Supervision

02/2023 - today	Co-supervising Ph.D. students, Kassel
08/2022 - 08/2026	Mentoring Bachelor's and Master's students, 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

13. Using Machine Learning to Enhance Pandemic Modeling: Case study of COVID-19 Dynamics in Ghana (with A. Meister, I. Azure) Journal of Mathematics in Industry (2026) [DOI]
12. The Lax–Wendroff theorem for Patankar-type methods applied to hyperbolic conservation laws (with J. Bender, D. Torlo, P. Öffner) Computers & Fluids (2026) [DOI]
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] (Not available due to an embargo - will be published soon by Springer.) Arxiv-version: [DOI]

Preprints

2. Flux-Balanced Patankar-type Schemes for the Compressible Euler Equations (Accepted in Communications on Applied Mathematics and Computation (CAMC)) (with A. Meister, D. Torlo, C.-W. Shu) (2026) [DOI]
1. A Positivity-Preserving Relaxation Algorithm (with H. Ranocha, C.-W. Shu) (2026) [DOI]

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