Doubly quasi-consistent parallel explicit peer methods with built-in global error estimation / G. Yu. Kulikov; R. Weiner
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Doubly quasi-consistent parallel explicit peer methods with built-in global error estimation
Discovery
585787441
URN
urn:nbn:de:gbv:3:2-7923
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Publication history
Halle : Inst. für Mathematik, 2008
Content
Online-Ressource (PDF-Datei: 22 S., 0,65 MB)
Edition
Language
eng
Comment
Parallel als Buch-Ausg. erschienen
Abstract
Recently, Kulikov presented the idea of double quasi-consistency, which facilitates global error estimation and control, considerably. More precisely, a local error control implemented in such methods plays a part of the global error control at the same time. However, Kulikov studied only Nordsieck formulas and proved that there exists no doubly quasi-consistent scheme among those methods. Here, we prove that the class of doubly quasi-consistent formulas is not empty and present the first example of such sort. This scheme belongs to the family of superconvergent explicit two-step peer methods constructed by Weiner, Schmitt, Podhaisky and Jebens. We present a sample of s-stage doubly quasi-consistent parallel explicit peer methods of order s - 1 when s = 3. The notion of embedded formulas is utilized to evaluate efficiently the local error of the constructed doubly quasi-consistent peer method and, hence, its global error at the same time. Numerical examples of this paper confirm clearly that the usual local error control implemented in doubly quasi-consistent numerical integration techniques is capable of producing numerical solutions for user-supplied accuracy conditions in automatic mode.
Series
Reports ; 2008,18 ppn:584754027