Fast convergence pirkn-type pc methods with adams-type predictors^∗

^∗This work was partly supported by N.R.P.F.S.

Abstract

This paper discusses predictor–corrector iteration schemes (PC iteration schemes) based on direct collocatio–based Runge–Kutt–Nyström corrector methods (RKN corrector methods) for solving nonstiff initial-value problems (IVPs) for systems of special second-order differential equations y′′(t) = f(y(t)) Our approach is to regard the well-known parallel-iterated RKN methods (PIRKN methods) as PC iteration processes in which the simple, low-order last step value predictors are replaced with the high-order Adams-type predictors. Moreover, the param-eters of the new direct collocation-based RKN corrector methods are chosen in such a way that the convergence rate of the considered PC iteration processes is optimized. In this way, we obtain parallel PC methods with fast convergence and high-accurate predictions. Application of the resulting parallel PC methods to a few widely-used test problems reveals that the sequential costs are very much reduced when compared with the parallel and sequential explicit RKN methods from the literature.

Keywords:

• Runge–Kutta–Nyström methods
• Predictor–corrector methods
• Stability Parallelism

C.R. Category::

• G.1.7

^∗This work was partly supported by N.R.P.F.S.

^†Corresponding author.

^∗This work was partly supported by N.R.P.F.S.

^†Corresponding author.

Notes

^∗This work was partly supported by N.R.P.F.S.

^†Corresponding author.