Predictor-Corrector Iteration for Runge-Kutta-Nystrom Methods with Stepsize Control and Its Parallel Implementation

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  • きざみ幅制御機能を持つ予測子・修正子型Runge-Kutta-Nystrom 法とその並列計算機への実装
  • キザミハバ セイギョ キノウ オ モツ ヨソクシ シュウセイシガタ Runge

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Abstract

A parallel predictor-corrector method, which consists of an explicit block method and an implicit Runge-Kutta-Nystrom method, is developed for solving second order initial value problems of the form y″=f(x, y), y(x_0)=η, y′(x_0)=ζ. A stepsize strategy based on Milne's device and an adaptive scheme for the predictor-corrector iteration are proposed. The method is implemented on a KSR1 parallel computer, which is a distributed memory system with 32 processors. The numerical experiment on the computer shows that the most successful implementation achieves a peak performance of speed-up 7.6 when the number of processors is 18.

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