Delay dependent stability of a class of boundary value methods for delay differential equation (Q2786057)

The authors investigate delay dependent stability properties of a class of boundary value methods (BVMs) for linear delay differential equations NEWLINENEWLINE\[NEWLINEy'(t)=ay(t)+by(t-\tau)NEWLINE\]NEWLINE NEWLINEsubject to the initial condition \(y(t)=g(t)\) on \([-\tau,0]\). In the case of the extended trapezoidal rule of the second kind, delay dependent stability regions are displayed. Moreover, it is shown that the above trapezoidal scheme can preserve delay-dependent stability for the above test equation. The theoretical results are confirmed by numerical experiments.