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1974•Canadian Mathematical BulletinOpen access

A Singular Perturbation Problem and A Neutral Differential-Difference Equation

Edward Moore

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Abstract

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.

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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.

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Available abstract

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.

Key concepts: Mathematics, Differential equation, Constant (computer programming), Mathematical analysis, Taylor series, Constant coefficients, Perturbation (astronomy), Connection (principal bundle)

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