Abstract Selecting between explicit and implicit time marching schemes, as well as non-iterative explicit-implicit ones, is well understood on a linear stability basis. Implicit schemes are favored when either searching for steady-states or performing time accurate simulations of stiff equations due to their larger time steps. When nonlinear stability properties must be preserved, however, solution monotonicity is guaranteed by a time step restriction that puts into question the usefulness of implicit schemes. Five test cases are used in this paper for a comparative efficiency analysis of explicit, implicit and implicit-explicit Strong Stability Preserving (SSP) Runge-Kutta (RK) schemes. They indicate that explicit SSP-RK schemes are, in general, the most efficient ones. It is important to emphasize that great care must be exercised when generalizing these conclusions, since such an analysis is inherently software, hardware, numerics and model dependent. Nevertheless, this study provides the first systematic evidence in the literature confirming these trends, to the best of our knowledge. Finally, implicit-explicit SSP-RK schemes do perform well, even though they are not optimal. Hence, there is a need for the development of their optimal versions before any conclusions can be drawn about their efficiency.

中文翻译：

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显式、IMEX 和隐式强稳定性保持 Runge-Kutta 方案的比较分析

摘要 在线性稳定性的基础上，可以很好地理解显式和隐式时间推进方案以及非迭代显式-隐式方案之间的选择。由于其较大的时间步长，隐式方案在搜索稳态或执行刚性方程的时间精确模拟时受到青睐。然而，当必须保留非线性稳定性属性时，解决方案的单调性由时间步长限制保证，这使隐式方案的有用性受到质疑。本文使用五个测试用例对显式、隐式和隐式-显式强稳定性保持 (SSP) Runge-Kutta (RK) 方案进行比较效率分析。它们表明显式 SSP-RK 方案通常是最有效的方案。重要的是要强调在概括这些结论时必须非常小心，因为这样的分析本质上是依赖于软件、硬件、数字和模型的。尽管如此，据我们所知，这项研究提供了文献中第一个系统性证据，证实了这些趋势。最后，隐式-显式 SSP-RK 方案确实表现良好，即使它们不是最优的。因此，在对它们的效率得出任何结论之前，需要开发它们的最佳版本。即使它们不是最佳的。因此，在对它们的效率得出任何结论之前，需要开发它们的最佳版本。即使它们不是最佳的。因此，在对它们的效率得出任何结论之前，需要开发它们的最佳版本。