Stability of Runge-Kutta methods for linear delay differential equations (Q1592352)

The paper is concerned with the stability of Runge-Kutta methods applied to the complex linear scalar delay differential equation \[ y'(t) = a y(t) + b y(t-1) \;, \] with \( a \) and \( b \) complex values. This is known in the literature as \(\tau\)-stability. The main contributions of the author are the characterization of \(\tau\)-stable Runge-Kutta methods and a proof that the implicit Euler method is \(\tau\)-stable.