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Vietnam Journal of Mathematics 34:1(2006) 95-108

 Efficiency of Embedded Explicit Pseudo Two-Step RKN Methods on a Shared Memory Parallel Computer

N. H. Cong, H. Podhaisky, and R. Weiner

Abstract.  The aim of this paper is to construct two embedded explicit pseudo two-step RKN methods (embedded EPTRKN methods) of order 6 and 10 for nonstiff initial-value problems (IVPs) y''(t) = f(t, y(t)), y(t0) = y0,  y'(t0) = 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 speed-up 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.

 

 

 

 

 

 

 

 

 

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