Parallel one-step methods with minimal parallel stages
Abstract: "The computing time of one-step methods for the numerical solution of initial-value problems y'(x) = f(x, y); y(x₀) = y₀ is closely related to the order of the approximation and the number of evaluations of f per unit step called stages. If parallel computers are used, the defini...
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| Format: | UnknownFormat |
| Sprache: | eng |
| Veröffentlicht: |
München
1992
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| Schriftenreihe: | Technische Universität <München>: TUM-MATH
9210 |
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Tag hinzufügen | Zusammenfassung: | Abstract: "The computing time of one-step methods for the numerical solution of initial-value problems y'(x) = f(x, y); y(x₀) = y₀ is closely related to the order of the approximation and the number of evaluations of f per unit step called stages. If parallel computers are used, the definition of stages has to be adapted, as many evaluations can be done simultaneously. For explicit Runge-Kutta (RK) methods of order p the minimal number of parallel stages s[subscript p] is known to be s[subscript p] = p. Here the result is generalized for any arbitrary type of explicit one-step method. For some important clases [sic] of implicit methods like implicit Runge-Kutta (IRK) methods, diagonal implicit Runge- Kutta (DIRK) methods, singly diagonal implicit Runge-Kutta (SDIRK) methods and semi-implicit Runge-Kutta (SIRK) methods, the same technique can be applied and leads to lower bounds of the minimal ps. Finally we show that for Rosenbrock-Wanner (ROW) methods s[subscript p] = p - 1 is optimal." |
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| Beschreibung: | 12 S. |