Abstract. The aim of this paper is to
construct two embedded explicit pseudo twostep RKN methods (embedded
EPTRKN methods) of order 6 and 10 for nonstiff initialvalue problems
(IVPs) y''(t) = f(t, y(t)), y(t_{0) }= y_{0},
y'(t_{0})
= y'_{0} and investigate
their efficiency on parallel computers. For these two embedded EPTRKN
methods and for expensive problems, the parallel implementation on a shared
memory parallel computer gives a good speedup with respect to the
sequential one. Furthermore, for numerical comparisons, we solve three test
problems taken form the literature by the embedded EPTRKN methods and the
efficient nonstiff code ODEX2 running on the same shared memory parallel
computer. Comparing computing times for accuracies received shows that the
two new embedded EPTRKN methods are superior to the code ODEX2 for all the
test problems.
