A new optimized non-FSAL embedded Runge–Kutta–Nystrom algorithm of orders 6 and 4 in six stages

Abstract

In the current paper a new 4-parameter Runge–Kutta–Nystrom (RKN) family of the non-FSAL type is constructed. The strategy used for the construction is based on the criteria listed by Dormand et al. [IMA J. Numer. Anal. 7 (1987) 235]. By an appropriate choice of the free parameters we obtained an optimized non-FSAL RKN 6(4) 6 embedded algorithm. The coefficients of this algorithm are obtained by writing a program in MACSYMA (MACSYMA Reference Manual). Test results indicate the superiority of the new algorithm relative to the RKN 6(4) 6 FM algorithm of the FSAL type of Dormand et al.