Practically, predictor-corrector methods for the solution of differential equations are widely used. In these numerical methods, the question of stability is most important. For a single differential equation Crane and Lambert (1962) studies the stability of a fourth-order generalized corrector formula; Chase (1962) and subsequently Emanuel (1963) demonstrated for particular methods that the overall integration procedure does not generally possess the same stability properties as the corrector except when the step of integration tends to zero. In the present paper it is shown that it is possible to develop a necessary and sufficient condition for the stability of general predictor-corrector methods for the solution of systems of differential equations.

This paper tackles the problem of the region of stability of the fourth order Runge-Kutta method for the solution of systems of differential equations. Such a region can be characterized by means of linear transformation but can not be given in a closed form. In the present case, the region has been determined using the electronic digital computer Z22.