论文标题
非振荡和积极保留时间整合方案的必要条件
A necessary condition for non oscillatory and positivity preserving time-integration schemes
论文作者
论文摘要
修改的Patankar（MP）方案是保守的，线性的隐式和无条件积极性的保留时间整合方案，该方案是为生产毁灭系统构建的。对于此类方案，经典稳定性分析不会产生有关性能的任何信息。最近，已经提出了两种不同的技术来研究MP方案的性质。在Izgin等人中。 [ESAIM：M2AN，56（2022）]，受动力学系统的启发，在Torlo等人中已经研究了此类方案的Lyapunov稳定性。 [应用。 numer。 Math。，182（2022）]他们的振荡行为已经进行了研究。在这项工作中，我们研究了振荡行为与Lyapunov稳定性之间的联系，并证明了Lyapunov稳定性函数的条件是避免振荡的。我们在几个数值测试上验证了我们的理论结果。
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.
