HYBRID METHODS IN THE NUMERICAL-SOLUTION OF VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS

The theory of hybrid methods in ordinary differential equations is extended to deal with the numerical solution of Volterra integro-differential equations. A convergence proof is given in which it is attempted to follow the convergence proof given in Gragg & Stetter (1964) for the numerical solution of y1 = f(x, y), y(0) = yo, as closely as possible. Several numerical examples are included. Also the stability polynomial of a hybrid method using two off-step points and the stability regions for two particular methods are given. © 1982 Academic Press Inc. (London) Limited.