具有强稳定性保持显式部分的变换隐式-显式DIMSIMs
Transformed implicit-explicit DIMSIMs with strong stability preserving explicit part
AI总结：
本文研究了具有强稳定性保持显式部分的隐式-显式DIMSIMs，探讨了其稳定性特性，并提供了具有良好稳定性质的四阶SSP IMEX DIMSIMs示例。
摘要：
对于许多科学和工程中建模的问题的微分方程组，右端通常可以自然地分成两部分，其中一部分是非刚性或轻微刚性的，而另一部分是刚性的。此类系统可以有效地通过一类隐式-显式（IMEX）对角隐式多阶段积分方法（DIMSIMs）来处理，其中刚性部分通过隐式公式积分，而非刚性部分通过显式公式积分。本文将构造显式部分具有强稳定性保持（SSP）性质的方法，并且隐式部分为A-或L-稳定的IMEX方法。此外，还将研究这些方法在隐式和显式部分相互作用时的稳定性。更具体地说，将监测IMEX方案的绝对稳定性区域大小，假设隐式部分为A-或L-稳定的。最后，本文将提供具有良好稳定性质的四阶SSP IMEX DIMSIMs的示例。
英文摘要：
For many systems of differential equations modeling problems in science and engineering, there are often natural splittings of the right hand side into two parts, one of which is non-stiff or mildly stiff, and the other part is stiff. Such systems can be efficiently treated by a class of implicit-explicit (IMEX) diagonally implicit multistage integration methods (DIMSIMs), where the stiff part is integrated by implicit formula, and the non-stiff part is integrated by an explicit formula. We will construct methods where the explicit part has strong stability preserving (SSP) property, and the implicit part of the method is $A$-, or $L$-stable. We will also investigate stability of these methods when the implicit and explicit parts interact with each other. To be more precise, we will monitor the size of the region of absolute stability of the IMEX scheme, assuming that the implicit part of the method is $A$-, or $L$-stable. Finally we furnish examples of SSP IMEX DIMSIMs up to the order four with good stability properties.
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