Enclosure Methods as Applied to Linear Periodic ODEs and Matrices
Dr.-Ing. E. Adams, Dietmar Cordes, Hans Keppler · ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik · 1990
Abstract Concerning linear ODEs with periodic coefficients, enclosure methods are presented for the verification of (i) asymptotic stability of the homogeneous ODEs and (ii) the existence of periodic solutions of the nonhomogeneous ODEs. In the case of forcing stochastic “interval point processes”, (iii) the set of (classical) solutions and marginal distribution functions concerning this set are enclosed. A sufficient matrix test with respect to (i) is directly applicable for the verification of |λi| < 1 or Re (λi) < 0 for the eigenvalues λi or λi of related matrices. Numerical examples show the power of the presented enclosure methods, among others in applications concerning gear drive vibrations.