2018/08/28 by Miklós E. Mincsovics, Mincsovics, Miklós E.
Computer Science · Engineering · Mathematics · #65L06 #65L20 #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Numerical methods for differential equations #Power System Optimization and Stability
paper · doi:10.48550/arxiv.1808.09485
openalex publication_date 2018/08/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Strongly and weakly stable linear multistep methods can behave very differently. The latter class can produce spurious oscillations in some of the cases for which the former class works flawlessly. The main question is if we can find a well defined property which clearly tells the difference between them. There are many explanations from different viewpoints. We cite Spijker's example which shows that the explicit two step midpoint method is unstable with respect to the Spijker norm. We show that this result can be extended for the general weakly stable case.