Errata for "Hybrid Methods in the Numerical Solution of Volterra Integro--differential Equations"

In the above paper [IMA J. num. Analysis (1982) 2, 21–35]the theory of hybrid methods in ordinary differential equationswas extended to deal with the numerical solution of Volterraintegro—differential equations. The stability regionsfor two particular methods were given. The region given in Fig.1(b) (ibid., p. 34) is incorrect. Our purpose is to providethe correct stability region and to correct some associatederrors. We employ the notation of the original paper.     

Hybrid Methods in the Numerical Solution of Volterra Integro-differential Equations

The theory of hybrid methods in ordinary differential equationsis extended to deal with the numerical solution of Volterraintegro-differential equations. A convergence proof is givenin which it is attempted to follow the convergence proof givenin Gragg & Stetter (1964) for the numerical solution ofy¹ = f(x, y), y(0) = y_o, as closely as possible. Several numericalexamples are included. Also the stability polynomial of a hybridmethod using two off-step points and the stability regions fortwo particular methods are given.