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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Bibliographic Details

Main Author:	Kiehl, Martin (Author)
Format:	Book
Language:	English
Published:	München 1992
Series:	Technische Universität <München>: TUM-MATH 9210
Subjects:	Runge-Kutta formulas
Summary:	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."
Physical Description:	12 S.