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.

由于在推导微分方程的能量或熵估计时，零件积分是一种重要的工具，因此可以推测，某些形式的零件求和（SBP）属性涉及可证明的稳定数值方法。本文通过提出一门新颖的A类为这一主题做出了贡献稳定的SBP时间积分方法，也可以将其重新构造为隐式Runge-Kutta方法。与现有的使用同时逼近项弱地施加初始条件的SBP时间积分方法相比，新方案使用投影方法在不破坏SBP属性的情况下强烈施加初始条件。新的方法类别包括经典的Lobatto IIIA配置方法，以前没有公式化为SBP方案。另外，开发了包括经典Lobatto IIIB配置方法的相关SBP方案。