Abstract
The aim of the present paper is to construct a class of two-step Runge-Kutta methods of arbitrarily high order for application to parallel computers. Starting with ans-stage implicit two-step Runge-Kutta method of orderp withk=p/2 implicit stages, we apply the highly parallel predictor-corrector iteration process in P(EC)mE mode. In this way, we obtain an explicit two-step Runge-Kutta method that has orderp for allm and that requiresk(m+1) right-hand side evaluations per step of which eachk evaluation can be computed in parallel. By a number of numerical experiments we show the superiority of the parallel predictor-corrector methods proposed here over parallel method available in the literature.
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These investigations were supported by the (National) Research Programs for Fundamental Sciences.
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Cong, N.h., Mitsui, T. A class of explicit parallel two-step Runge-Kutta methods. Japan J. Indust. Appl. Math. 14, 303–313 (1997). https://doi.org/10.1007/BF03167270
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DOI: https://doi.org/10.1007/BF03167270