Explicit Runge–Kutta–Nyström methods for the numerical solution of second order linear inhomogeneous IVPs

Runge–Kutta–Nyström (RKN) methods for the numerical solution of inhomogeneous linear initial value problems with constant coefficients are considered. A general procedure to construct explicit s-stage RKN methods with maximal order p=s+1, similar to the developed by the authors (Montijano et al., 2023) for the class of second order IVP under consideration, depending on the nodes ci,i=1,…,s is presented. This procedure requires only the solution of successive linear equations in the elements aij, 1≤j