Abstract: "An iteration scheme is described to solve the implicit relations that result from the application of an implicit integration method to an initial value problem (IVP). In this iteration scheme the amount of implicitness is still free so as to comprise a large variety of methods, runni...

Ausführliche Beschreibung

Bibliographische Detailangaben

Hauptverfasser:	Houwen, Pieter J. van (VerfasserIn), Sommeijer, Ben P. ca. 20. Jh (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	Amsterdam 1992
Schriftenreihe:	Centrum voor Wiskunde en Informatica <Amsterdam> / Afdeling Numerieke Wiskunde: Report NM 1992,18
Schlagworte:	Numerical analysis
Zusammenfassung:	Abstract: "An iteration scheme is described to solve the implicit relations that result from the application of an implicit integration method to an initial value problem (IVP). In this iteration scheme the amount of implicitness is still free so as to comprise a large variety of methods, running from fully explicit (functional iteration) to fully implicit (Newton's method). In the intermediate variants (the so-called Jacobi-type methods), the influence of the Jacobian matrix of the problem is gradually increased. Special emphasis is placed on the 'stage-value- Jacobi' iteration which uses only the diagonal of the Jacobian matrix Therefore, the convergence of this method crucially depends on the diagonally [sic] dominance of the Jacobian. Another characteristic of this scheme is that it allows for massive parallelism: For a d- dimensional IVP, d uncoupled systems of dimension s have to be solved, where s is the number of stages in the underlying implicit method (e.g., an s-stage Runge-Kutta method). Hence, on a parallel architecture with d processors (d>>1), we may expect an efficient process (for high- dimensional problems).
Beschreibung:	12 S.