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Enclosure Methods as Applied to Linear Periodic ODEs and Matrices
Author(s) -
Adams Prof. Dr.Ing. E.,
Cordes D.,
Keppler H.
Publication year - 1990
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19900701212
Subject(s) - enclosure , ode , mathematics , eigenvalues and eigenvectors , matrix (chemical analysis) , mathematical analysis , stability (learning theory) , set (abstract data type) , homogeneous , physics , computer science , combinatorics , telecommunications , materials science , quantum mechanics , machine learning , composite material , programming language
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 |λ i | < 1 or Re (λ i ) < 0 for the eigenvalues λ i or λ i of related matrices. Numerical examples show the power of the presented enclosure methods, among others in applications concerning gear drive vibrations.