For backward differentiation formulae (BDF) applied to gradient flows of semiconvex functions, quadratic stability implies the existence of a Lyapunov functional. We compute the maximum time step which can be derived from quadratic stability for the 3-step BDF method (BDF3). Applications to the asymptotic behaviour of sequences generated by the BDF3 scheme are given.

中文翻译：

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BDF3方案应用于梯度流的最大时间步长

对于应用于半凸函数的梯度流的后向微分公式（BDF），二次稳定性意味着存在Lyapunov函数。我们为3步BDF方法（BDF3）计算可以从二次稳定性得出的最大时间步长。给出了由BDF3方案生成的序列的渐近行为的应用。