Runge-Kutta-Nystrom triples

Abstract

The embedded Runge-Kutta-Nystrom process for the numerical solution of the special second-order initial-value problem can be extended by the addition of “dense” formulae for both y and y′ which yield solutions at points within the normal step intervals. As for Runge-Kutta methods two modes of implementation are possible and it is shown that these are equivalent under certain conditions. The cases of “dense” formulae applied to RKN4(3) and RKN6(4) families are considered and test results are presented.