Modified Patankar Linear Multistep Methods for Production-Destruction Systems
Abstract Modified Patankar schemes are linearly implicit time integration methods designed to be unconditionally positive and conservative. In the present work we extend the Patankar-type approach to linear multistep methods and prove that the resulting discretizations retain, with no restrictions on the step size, the positivity of the solution and the linear invariant of the continuous-time system. Moreover, we provide results on arbitrarily high order of convergence and we introduce an embedding technique for the Patankar weights denominators to achieve it.
Authors
- Antonia Vecchio (ORCID: https://orcid.org/0000-0003-2746-7535)
- Eleonora Messina (ORCID: https://orcid.org/0000-0003-4545-6266)
- Giuseppe Izzo (ORCID: https://orcid.org/0000-0003-1412-8702)
- Mario Pezzella (ORCID: https://orcid.org/0000-0002-1869-945X)
Institutions
- Istituto Nazionale di Alta Matematica Francesco Severi (IT)
- Federico II University Hospital (IT)
- Institute of Protein Biochemistry (IT)
- National Research Council (IT)
- University of Naples Federico II (IT)
Publication Details
- Journal
- Journal of Scientific Computing
- Published
- 2025-02-05
- DOI
- https://doi.org/10.1007/s10915-025-02804-5
- Citations
- 6
- Primary Topic
- Advanced Control Systems Optimization
- Type
- article
- Field-Weighted Citation Impact
- 7.29
Funders
- Università degli Studi di Napoli Federico II
- Istituto Nazionale di Alta Matematica "Francesco Severi"
- Ministero dell'Università e della Ricerca
- Gruppo Nazionale per il Calcolo Scientifico