On the numerical solution of a semilinear elliptic eigenproblem of Lane-Emden type, (II): Numerical experiments

  • In this second part of our two-part article, we present and discuss the correponding numerical results from implementations of the numerical algorithms described in the first part. With these results, we observed that (1) operator splitting applied to the associated time-dependent problem is suitable for solving only the first eigenproblem, (2) among those tried, the perturbation and arclength continuation approach was the sole effective and robust approach for solving higher eigenproblems, (3) on the eigenproblems for which Newton's method converged, it was without question the most efficient.

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Author:Fritz J. II. Foss, Roland GlowinskiGND, Ronald H. W. HoppeGND
Frontdoor URLhttps://opus.bibliothek.uni-augsburg.de/opus4/518
Series (Serial Number):Preprints des Instituts für Mathematik der Universität Augsburg (2007-11)
Publishing Institution:Universität Augsburg
Contributing Corporation:Department of Mathematics, University of Houston
Release Date:2007/05/30
Tag:semilinear eigenproblem; operator splitting; arclength continuation; least squares
GND-Keyword:Semilineares Eigenwertproblem; Operator-Splitting-Verfahren; Fortsetzungsmethode; Methode der kleinsten Quadrate
Institutes:Mathematisch-Naturwissenschaftlich-Technische Fakultät
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik
Mathematisch-Naturwissenschaftlich-Technische Fakultät / Institut für Mathematik / Lehrstuhl für Numerische Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik