论文标题
$ a $ stable的新课程按零件时间集成方案（具有强烈初始条件）
A New Class of $A$ Stable Summation by Parts Time Integration Schemes with Strong Initial Conditions
论文作者
论文摘要
由于在得出微分方程的能量或熵估计时，按零件进行集成是一个重要的工具，因此可以猜测，某种形式的零件总和（SBP）属性与可证明的稳定数值方法有关。本文通过提出新颖的$ a $ a $ stable SBP时间集成方法来贡献此主题，该方法也可以作为隐式runge-kutta方法重新构成。与使用同时近似项的现有SBP时间集成方法相反，将初始条件强加于初始条件，新方案使用投影方法强烈强烈强制强烈强烈地强制强制强烈的初始条件，而不会破坏SBP属性。新的方法包括经典的Lobatto IIIA搭配方法，以前不是以SBP方案的配制。此外，开发了一个相关的SBP方案，包括经典的Lobatto IIIB搭配方法。
Since integration by parts is an important tool when deriving energy or entropy estimates for differential equations, one may conjecture that some form of summation by parts (SBP) property is involved in provably stable numerical methods. This article contributes to this topic by proposing a novel class of $A$ stable SBP time integration methods which can also be reformulated as implicit Runge-Kutta methods. In contrast to existing SBP time integration methods using simultaneous approximation terms to impose the initial condition weakly, the new schemes use a projection method to impose the initial condition strongly without destroying the SBP property. The new class of methods includes the classical Lobatto IIIA collocation method, not previously formulated as an SBP scheme. Additionally, a related SBP scheme including the classical Lobatto IIIB collocation method is developed.
