A fifth-order interpolant for the Dormand and Prince Runge-Kutta method

摘要

A family of fifth-order interpolants for the fifth-order solution provided by the Dormand and Prince Runge-Kutta pair RK5(4)7M which requires two additional function evaluations per step is presented. An optimal interpolant in this family has been determined by choosing the parameters to minimize the leading coefficients of the local truncation error of the continuous solution. Some numerical experiments with the nonstiff DETEST problems show that the proposed optimal method has a good interpolatory behavior.