Stability of some continuously imbedded Runge-Kutta methods of Sarafyan (Q1092626)

\textit{D. Sarafyan} [Comput. Math. Appl. 10, 139-159 (1984; Zbl 0552.65056)] has developed novel explicit Runge-Kutta methods for the initial value problem: \(y'(t)=f(t,y(t))\), \(y(t_ 0)=y_ 0\). Associated with each method is an imbedded interpolating polynomial. In this paper two continuously imbedded methods are considered; it is shown that the polynomials possess the stability properties of the Runge-Kutta methods. That makes them useful for the problem of dense output and for rootfinding.