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arXiv · 2211.08905

A necessary condition for non oscillatory and positivity preserving time-integration schemes

Thomas Izgin·Philipp Öffner·Davide Torlo
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Abstract

Modified Patankar (MP) schemes are conservative, linear implicit and unconditionally positivity preserving time-integration schemes constructed for production-destruction systems. For such schemes, a classical stability analysis does not yield any information about the performance. Recently, two different techniques have been proposed to investigate the properties of MP schemes. In Izgin et al. [ESAIM: M2AN, 56 (2022)], inspired from dynamical systems, the Lyapunov stability properties of such schemes have been investigated, while in Torlo et al. [Appl. Numer. Math., 182 (2022)] their oscillatory behaviour has been studied. In this work, we investigate the connection between the oscillatory behaviour and the Lyapunov stability and we prove that a condition on the Lyapunov stability function is necessary to avoid oscillations. We verify our theoretical result on several numerical tests.

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Thomas Izgin, Philipp Öffner, Davide Torlo. 2022-11-16. A necessary condition for non oscillatory and positivity preserving time-integration schemes. https://arxiv.org/abs/2211.08905

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