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A Singular Perturbation Problem and A Neutral Differential-Difference Equation

Published online by Cambridge University Press:  20 November 2018

Edward Moore
Edward Moore*
Affiliation:
Faculty of Engineering and Applied Science, Memorial University Of Newfoundland, St. John’s, Newfoundland, Canada
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Vasil’eva, [2], demonstrates a close connection between the explicit formulae for solutions to the linear difference equation with constant coefficients

(1.1)

where z is an n-vector, A an n×n constant matrix, τ>0, and a corresponding differential equation with constant coefficients

(1.2)

(1.2) is obtained from (1.1) by replacing the difference z(t—τ) by the first two terms of its Taylor Series expansion, combined with a suitable rearrangement of the terms.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 17 , Issue 1 , 01 March 1974 , pp. 77 - 83
Copyright
Copyright © Canadian Mathematical Society 1974

References

1. Levinson, N., Perturbations of Discontinuous Solutions of Non-linear Systems of Differential Equations, Acta Math., 82, 71-106.Google Scholar
2. Vasil'eva, A. B., Correspondence Between Certain Properties of Solutions of Linear Difference Systems and Systems of Ordinary Linear Differential Equations, Trudy Sem. Teor. Differential Uravnenii S Otklon. Argumentom., Univ. Druzby Narodov Patrisa Lumumby, 5 (1967), 21-44.Google Scholar
3. Wasow, W., Asymptotic Expansions for Ordinary Differential Equations, Interscience Publishers, New York, 1965.Google Scholar