Error of one-leg methods for singular perturbation problems with delays (Q1566058)

The paper deals with the error behaviour of A-stable one-leg integration schemes applied to the singularly perturbed differential-delayed system \(x'(t)= f(z(t))\), \(\varepsilon y'(t)= g(z(t))\) for \(t\in [0, T]\) and \(x(t)= \varphi(t)\), \(y(t)= \psi(t)\) for \(t\leq 0\), where \(z(t)= (x(t), x(t-\tau),y(t), y(t-\tau))\) and \(\varepsilon> 0\) is a small parameter.