论文标题
部分可观测时空混沌系统的无模型预测
Stability of variable-step BDF2 and BDF3 methods
论文作者
论文摘要
我们证明，两步向后分化公式（BDF2）方法在任意时间网格上是稳定的。如果几乎所有相邻的步骤比小于2.553，则可变步骤BDF3方案是稳定的。这些结果放松了文献中严重的网格限制，并对可变的阶段BDF方法有了新的了解。我们的主要工具包括离散的正交卷积内核和椭圆型矩阵标准。
We prove that the two-step backward differentiation formula (BDF2) method is stable on arbitrary time grids; while the variable-step BDF3 scheme is stable if almost all adjacent step ratios are less than 2.553. These results relax the severe mesh restrictions in the literature and provide a new understanding of variable-step BDF methods. Our main tools include the discrete orthogonal convolution kernels and an elliptic-type matrix norm.
