论文标题
六步BDF方法的能量技术
The energy technique for the six-step BDF method
论文作者
论文摘要
结合Grenander-Szegö定理，我们观察到，乘数上的阳性条件轻松，比Nevanlinna-odeh乘数的基本％基本要求温和，其组件的绝对值的总和严格远小于$ 1 $，使能量技术适用于Babd Fore的稳定性分析，以供Babdforoloical分析，以供Babdforoloics分析。这对于不存在Nevanlinna-Odeh乘数的六步BDF方法特别有用。我们介绍了满足六步BDF方法的阳性属性的乘数，并确立了抛物线方程方法的稳定性。
In combination with the Grenander--Szegö theorem, we observe that a relaxed positivity condition on multipliers, milder than the basic %fundamental requirement of the Nevanlinna--Odeh multipliers that the sum of the absolute values of their components is strictly less than $1$, makes the energy technique applicable to the stability analysis of BDF methods for parabolic equations with selfadjoint elliptic part. This is particularly useful for the six-step BDF method for which no Nevanlinna--Odeh multiplier exists. We introduce multipliers satisfying the positivity property for the six-step BDF method and establish stability of the method for parabolic equations.
