GENERATION OF HIGH-ORDER INTERPOLANTS FOR EXPLICIT RUNGE-KUTTA PAIRS

Explicit Runge-Kutta pairs can be enhanced by providing them with inte rpolants. Enhancements include the ability to estimate and control the defect, to produce dense output, and to calculate past values in dela y differential equations. The coefficients of an interpolant are easil y generated by bootstrapping on the order conditions. However, the gen eration of high-order interpolants requires a large number of arithmet ic operations. We describe an efficient algorithm for the generation o f high-order interpolants and illustrate the use of the algorithm with three applications.