Runge-Kutta Type Procedures of Order of Accuracy n + 4 (N>2) with Three Nodes for Numerical Integration of First-Order Differential Equations

摘要

By transformation, E. Fehlberg reduced integration of a first-order differential equation: dz/dx=F(x,z), with initial condition: z(x 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 n+4 (n>or =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.