RUNGE-KUTTA TYPE PROCEDURES OF ORDER OF ACCURACY N + 4 (N>2) WITH THREE NODES FOR NUMERICAL INTEGRATION OF FIRST-ORDER DIFFERENTIAL EQUATIONS,
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By transformation, E. Fehlberg reduced integration of a first-order differential equation dzdxFx,z, with initial condition zx sub 0 z sub 0, to integration of another first-order differential equation. This allows the establishment of Runge-Kutta type operations of sixth-order accuracy for numerical integration of the transformed differential equation. In the first part of this paper the Fehlberg transformation is extended to allow the establishment of Runge-Kutta procedures of eighth-order accuracy with three nodes for numerical integration of the transformed differential equation. Then the above transformations are generalized to permit establishment of Runge-Kutta procedures of order of accuracy n4 nor 2 with three nodes for numerical integration of the transformed differential equation. The nodes and coefficients in the formulas used for application of these procedures are rational numbers.