Characterization of a class of P-stable methods for differential equations of second order (Q1102078)

This paper extends and partially modifies earlier results of \textit{M. M. Chawla} and \textit{B. Neta} [J. Comput. Appl. Math. 15, 213-223 (1986; Zbl 0599.65044)] on families of P-stable methods for second order differential equations of the form \(y''=f(x,y)\). In fact, Chawla and Neta used a sufficient condition for P-stability and therefore their characterization of the P-stable formulas in their family of methods is incomplete. Here the stability analysis of his family of formulas is completed using necessary and sufficient conditions for P-stability.