Stability analysis of one-step methods for neutral delay-differential equations (Q1102710)

Stability properties of one-step methods for neutral functional- differential equations \[ (1)\quad y'(t)=f(t,y(t),y(t-h),y'(t-h)),\quad t\geq 0;\quad y(t)=g(t),\quad -h\leq t\leq 0. \] Stability regions for Runge-Kutta methods are determined relative to the test equation \(y'(t)=ay(t)+by(t-h)+cy'(t-h)\), where a, b, c are complex parameters. The influence of the approximation of y' on the stability properties of one- step methods for solving (1) is also studied.