ON SOME EXTENSIONS OF A FEHLBERG TRANSFORMATION,
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This paper gives a class of procedures of the fourth order of accuracy, a fifth order procedure and a class of procedures of the sixth order of accuracy for numerically integrating differential equations of the first order. For these, there are used two extensions of a transformation given by E. Fehlberg which must be made on the differential equation. The application of those procedures requires a minimum number of substitutions in the transformed differential equation. Thus, for applying procedures of the fourth and fifth orders of accuracy, a single substitution is necessary, and for applying procedures of the sixth order of accuracy, two substitutions in the transformed differential equation are required.