Abstract: "From a theoretical point of view, collocation-type Runge-Kutta methods of collocation type belong to the most attractive step- by-step methods for integrating stiff problems. These methods combine excellent stability features with the property of superconvergence at the step points....

Ausführliche Beschreibung

Bibliographische Detailangaben

Hauptverfasser:	Houwen, Pieter J. van der (VerfasserIn), Sommeijer, Ben P. ca. 20. Jh (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	Amsterdam 1993,10
Schriftenreihe:	Centrum voor Wiskunde en Informatica <Amsterdam> / Afdeling Numerieke Wiskunde: Report NM 1993,10
Schlagworte:	Runge-Kutta formulas
Zusammenfassung:	Abstract: "From a theoretical point of view, collocation-type Runge-Kutta methods of collocation type belong to the most attractive step- by-step methods for integrating stiff problems. These methods combine excellent stability features with the property of superconvergence at the step points. Like the IVP itself, they only need the given initial value without requiring additional starting values, and therefore are a natural discretization of the initial-value problem. On the other hand, from a practical point of view, these methods have the drawback of requiring in each step the solution of a system of equations of dimension sd, s and d being the number of stages and the dimension of the initial-value problem, respectively. In contrast, linear multistep methods, the main competitor of Runge-Kutta methods, require the solution of systems of dimension d However, parallel computers have changed the scene and have motivated us to design parallel iteration methods for solving the implicit systems in such a way that the resulting methods become efficient step-by- step methods for integrating stiff initial-value problems.
Beschreibung:	14 S.