Patankar-type schemes are linearly implicit time integration methods designed to be unconditionally positivity-preserving. However, there are only little results on their stability or robustness. We suggest two approaches to analyze the performance and robustness of these methods. In particular, we demonstrate problematic behaviors of these methods that, even on very simple linear problems, can lead to undesired oscillations and order reduction for vanishing initial condition. Finally, we demonstrate in numerical simulations that our theoretical results for linear problems apply analogously to nonlinear stiff problems.

Issues with positivity-preserving Patankar-type schemes / Torlo, D.; Offner, P.; Ranocha, H.. - In: APPLIED NUMERICAL MATHEMATICS. - ISSN 0168-9274. - 182:(2022), pp. 117-147. [10.1016/j.apnum.2022.07.014]

Issues with positivity-preserving Patankar-type schemes

Torlo, D.;
2022-01-01

Abstract

Patankar-type schemes are linearly implicit time integration methods designed to be unconditionally positivity-preserving. However, there are only little results on their stability or robustness. We suggest two approaches to analyze the performance and robustness of these methods. In particular, we demonstrate problematic behaviors of these methods that, even on very simple linear problems, can lead to undesired oscillations and order reduction for vanishing initial condition. Finally, we demonstrate in numerical simulations that our theoretical results for linear problems apply analogously to nonlinear stiff problems.
2022
182
117
147
https://arxiv.org/abs/2108.07347
Torlo, D.; Offner, P.; Ranocha, H.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/131394
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