2023/07/27 by Douglas R. Anderson, Masakazu Onitsuka, Anderson, Douglas R. +3
Mathematics · #34A30 #34D10 #34D20 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Equations Stability Results #Nonlinear Differential Equations Analysis #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.2307.15102
openalex publication_date 2023/07/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This study deals with the Ulam stability of non-autonomous linear differential systems without assuming the condition that they admit an exponential dichotomy. In particular, the best (minimal) Ulam constants for two-dimensional non-autonomous linear differential systems with generalized Jordan normal forms are derived. The obtained results are applicable not only to systems with solutions that exist globally on (-∞,∞), but also to systems with solutions that blow up in finite time. New results are included even for constant coefficients. A wealth of examples are presented, and approximations of node, saddle, and focus are proposed. In addition, this is the first study to derive the best Ulam constants for non-autonomous systems other than periodic systems.