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

Abstract

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.