Multistep Methods With Modified Predictors and Correctors

Abstract

In April, 1964, Gragg and Stetter published a set of numerical methods for solving y′ = f ( x , y ) which rely on some very accurate correctors, using a “nonstep” point within the interval of integration. However, the present authors found that this accuracy is largely lost unless one also uses accurate predictors, also using a “nonstep” point within an interval of integration, of the same order of accuracy as that of the correctors. Numerical examples indicate that on the average those differential equations tested can be solved by the method of the sixth order proposed in this paper in about two-thirds the time required by an Adams method of the same order.