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On the numerical solution of a semilinear elliptic eigenproblem of Lane–Emden type, II: Numerical experiments
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December 4, 2007
In this second part of our two-part article, we present and discuss the corresponding numerical results from implementations of the numerical algorithms described in the first part. With these results, we observed that
• operator splitting applied to the associated time-dependent problem is suitable for solving only the first eigenproblem,
• among those tried, the perturbation and arclength continuation approach was the sole effective and robust approach for solving higher eigenproblems,
• on the eigenproblems for which (undamped or damped) Newton's method converged, it was without question the most efficient.
Keywords: numerical method; Lane; Emden; semilinear; elliptic; eigenproblem; operator splitting; finite element; arclength continuation; least-squares; control; Newton's method
Received: 2007-February-22
Revised: 2007-May-05
Published Online: 2007-12-04
Published in Print: 2007-11-20
© de Gruyter 2007
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Articles in the same Issue
- Overlapping additive Schwarz preconditioners for isotropic elliptic problems with degenerate coefficients
- On the numerical solution of a semilinear elliptic eigenproblem of Lane–Emden type, II: Numerical experiments
- Unified edge-oriented stabilization of nonconforming FEM for incompressible flow problems: Numerical investigations
Keywords for this article
numerical method;
Lane;
Emden;
semilinear;
elliptic;
eigenproblem;
operator splitting;
finite element;
arclength continuation;
least-squares;
control;
Newton's method
Articles in the same Issue
- Overlapping additive Schwarz preconditioners for isotropic elliptic problems with degenerate coefficients
- On the numerical solution of a semilinear elliptic eigenproblem of Lane–Emden type, II: Numerical experiments
- Unified edge-oriented stabilization of nonconforming FEM for incompressible flow problems: Numerical investigations
