On rational function approximations to the exponential function with application to the practical solution of linear differential difference equation with constant coefficients

1956 ◽  
Author(s):  
Yudell L. Luke
Keyword(s):  
Difference Equation ◽  
Rational Function ◽  
Exponential Function ◽  
Practical Solution ◽  
Constant Coefficients ◽  
Differential Difference Equation ◽  
Linear Differential ◽  
Function Approximations

A Singular Perturbation Problem and A Neutral Differential-Difference Equation

1974 ◽  
Vol 17 (1) ◽  
pp. 77-83
Author(s):  
Edward Moore
Keyword(s):  
Difference Equation ◽  
Taylor Series Expansion ◽  
Linear Difference Equation ◽  
Constant Matrix ◽  
Perturbation Problem ◽  
Constant Coefficients ◽  
Explicit Formulae ◽  
Differential Difference Equation ◽  
The Difference ◽  
Image Position

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.

scholarly journals A transformation to linearity of some non-linear differential-difference equations

1982 ◽  
Vol 23 (4) ◽  
pp. 416-419
Author(s):  
A. J. Bracken
Keyword(s):  
Difference Equation ◽  
Difference Equations ◽  
Non Linear ◽  
Differential Difference Equation ◽  
Linear Differential

AbstractThe problem of solving a differential-difference equation with quadratic non-linearities of a certain type is reduced to the problem of solving an associated linear differential-difference equation.

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