Interpolants for Runge-Kutta-Nyström methods

Hermite interpolation polynomials are developed for use with low order Runge-Kutta-Nystrom methods in producing continuous approximate solutions to second order initial value problems. Polynomials of degrees five and four, which interpolate te solution and derivative components, respectively, are easily computable and require no extra stages. Interpolants of the next higher orders are obtained at the cost of two additional stages per integration step. The interpolation procedure is demonstrated using two recently developed Runge-Kutta-Nystrom methods. Numerical experimentation reveals some aspects of the performance of these interpolants.