Graphical Solutions for the Characteristic Roots of the First Order Linear Differential-Difference Equation

1979 ◽  
Vol 101 (1) ◽  
pp. 37-43 ◽  
Author(s):  
G. M. Sandquist ◽  
V. C. Rogers
Keyword(s):  
Difference Equation ◽  
Nuclear Reactor ◽  
Mathematical Proof ◽  
Practical Application ◽  
Numerical Accuracy ◽  
Order Linear ◽  
First Order ◽  
Characteristic Roots ◽  
Differential Difference Equation ◽  
Linear Differential

Approximate values for all the apparent real and imaginary characteristic roots of the general first order linear differential-difference equation are determined (primarily graphically) without mathematical proof. These approximate values may then be iterated in a convergent form of the characteristic equation to provide any desired numerical accuracy as shown in several examples. A practical application involving the kinetic behavior of nuclear reactor systems with delayed neutrons is given and compared with the more familiar system solutions.

scholarly journals Hyers-Ulam Stability of the First-Order Matrix Differential Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-7
Author(s):  
Soon-Mo Jung
Keyword(s):  
Differential Equations ◽  
Variable Coefficients ◽  
Linear Differential Equations ◽  
Ulam Stability ◽  
Order Linear ◽  
First Order ◽  
Matrix Differential Equations ◽  
Homogeneous Matrix ◽  
Linear Differential ◽  
Matrix Differential

We prove the generalized Hyers-Ulam stability of the first-order linear homogeneous matrix differential equationsy→'(t)=A(t)y→(t). Moreover, we apply this result to prove the generalized Hyers-Ulam stability of thenth order linear differential equations with variable coefficients.

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