Abstract: "We shall consider iteration processes for solving the implicit relations associated with implicit Runge-Kutta (RK) methods applied to stiff initial value problems (IVPs). The conventional approach for solving the RK equations uses Newton iteration employing the full righthand side Ja...

Ausführliche Beschreibung

Bibliographische Detailangaben

Hauptverfasser:	Houwen, Pieter J. van der (VerfasserIn), Sommeijer, Ben P. ca. 20. Jh (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	Amsterdam 1995
Schriftenreihe:	Centrum voor Wiskunde en Informatica <Amsterdam> / Afdeling Numerieke Wiskunde: Report NM 1995,6
Schlagworte:	Algorithms Initial value problems Iterative methods (Mathematics) Runge-Kutta formulas
Zusammenfassung:	Abstract: "We shall consider iteration processes for solving the implicit relations associated with implicit Runge-Kutta (RK) methods applied to stiff initial value problems (IVPs). The conventional approach for solving the RK equations uses Newton iteration employing the full righthand side Jacobian. For IVPs of large dimension, this approach is not attractive because of the high costs involved in the LU-decomposition of the Jacobian of the RK equations. Several proposals have been made to reduce these high costs. The most well-known remedy is the use of similarity transformations by which the RK Jacobian is transformed to a block-diagonal matrix whose blocks have the IVP dimension. In this paper we study an alternative approach which directly replaces the RK Jacobian by a block-diagonal or block-triangular matrix whose blocks themselves are block-triangular matrices. Such a grossly 'simplified' Newton iteration process allows for a considerable amount of parallelism. However, the important issue is whether this block-triangular approach does converge. It is the aim of this paper to get insight into the effect on the convergence of block-triangular Jacobian approximations."
Beschreibung:	16 S.