Abstract
In this paper a general interpolant for the Explicit Runge-Kutta methods is proposed. These interpolants are based on second derivatives on mesh-points of the integration interval, and first derivatives on interior points of each step. These first derivatives can be produced using lower order interpolants. Here an interpolant with 0(h 6) local truncation error for the fifth order solution used in RKF4(5) method is presented, with a cost of “about” one extra function evaluation per integration step.
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