Modified Patankar Linear Multistep methods for production-destruction systems
Numerical Analysis
2025-02-06 v1 Numerical Analysis
Dynamical 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 weight denominators to achieve it.
Cite
@article{arxiv.2407.12540,
title = {Modified Patankar Linear Multistep methods for production-destruction systems},
author = {Giuseppe Izzo and Eleonora Messina and Mario Pezzella and Antonia Vecchio},
journal= {arXiv preprint arXiv:2407.12540},
year = {2025}
}