On stability sets for numerical discretizations of neutral delay differential equations

Year, pages: 2015, 89 - 100

The paper discusses the $\Theta$-method discretization of the neutral delay differential equation \begin{equation*} y'(t) = a\,y(t) + b\,y(t-\tau) + c\,y'(t-\tau),\qquad t>0, \end{equation*} where $a,\,b,\,c$ are real constant coefficients and $\tau$ is a positive real lag. Using recent developments on stability of appropriate delay difference equations we give a complete description of stability sets for this discretization. Some of their properties and related comparisons with the stability set for the underlying neutral differential equation are discussed as well.

Čermák, J., Dražková, J. 2015. On stability sets for numerical discretizations of neutral delay differential equations. In Tatra Mountains Mathematical Publications, vol. 63, no.2, pp. 89-100. 1210-3195.

Čermák, J., Dražková, J. (2015). On stability sets for numerical discretizations of neutral delay differential equations. Tatra Mountains Mathematical Publications, 63(2), 89-100. 1210-3195.