Abstract.

A practical and accessible introduction to explicit Runge-Kutta-Nystr¨om (RKN) pairs for numerically approximate the solution of problems of the form ψ = φ(x, ψ) is given. The article is mainly built around five MATHEMATICA programs, that implement the algorithms for constructing RKN pairs of orders 4(3), 6(4), 7(5) and 8(6). Various pairs known from the relevant literature pairs are considered and it is shown how they arrive using the presented software. We also present new pairs of orders 6(4) and 8(6) sharing interesting properties.

Keywords:

initial value problem, special second order, numerical solution, explicit Runge-KuttaNystrom, MATHEMATICA