A Modification of Nordsieck's Method Using an ``Off-Step'' Point

In 1962, Nordsieck presented a series of numerical methods for solving ordinary differential equations which rely on Taylor's series, but which are equivalent to the correctors in the Adams methods. In a method of Nordsieck, simplifications, such as in the often desirable process of changing step size, are made, since it is unnecessary to store more than one previous step. In 1964, Gragg and Stetter published a series of numerical methods for solving ordinary differential equations which rely on very accurate correctors, using a “nonstep” point within the interval of integration. The method in the present paper is equivalent, for uniform step size, to one of these very accurate correctors but is in the form of Nordsieck. The strengths and weaknesses of the method are discussed.