A semidiscrete approximation scheme for neutral delay-differential equations (Q2865637)

The authors study a semidiscrete approximation scheme for neutral delay-differential equations. In particular, they extend the improved spline scheme by \textit{F. Kappel} and \textit{D. Salamon} [SIAM J. Control Optim. 25, 1082--1117 (1987; Zbl 0642.34065)] to neutral delay equations and prove semigroup convergence. The authors consider the first order spline scheme of Kappel and Salamon [loc. cit.], which was applied to retarded delay equations, and modify it to construct a scheme for neutral delay equations, and prove Trotter-Katto type semigroup convergence for the scheme. Numerical examples are given to illustrate the qualitative behavior of the approximation scheme.