Abstract

This paper considers the development of a class of one-point hybrid implicit methods for direct solution of general second order ordinary differential equations. The main predictors needed for the evaluation of the implicit methods are obtained to be of the same order with the methods at whatever hybrid point of collocation. The methods and their respective predictors are consistent and zero-stable. Numerical results are presented to show the accuracy of the methods.

Key words: One-point continuous hybrid, collocation and interpolation equations, grid point