Opuscula Math. 26, no. 2 (2006), 229-241
Opuscula Mathematica
Collocation methods for the solution of eigenvalue problems for singular ordinary differential equations
Winfried Auzinger
Ernst Karner
Othmar Koch
Ewa Weinmüller
Abstract. We demonstrate that eigenvalue problems for ordinary differential equations can be recast in a formulation suitable for the solution by polynomial collocation. It is shown that the well-posedness of the two formulations is equivalent in the regular as well as in the singular case. Thus, a collocation code equipped with asymptotically correct error estimation and adaptive mesh selection can be successfully applied to compute the eigenvalues and eigenfunctions efficiently and with reliable control of the accuracy. Numerical examples illustrate this claim.
Keywords: polynomial collocation, singular boundary value problems, linear and nonlinear eigenvalue problems.
Mathematics Subject Classification: 65L15, 34B24, 34L16, 65L10.
- Winfried Auzinger
- Vienna University of Technology, Institute for Analysis and Scientific Computing, Wiedner Hauptstrasse 8-10/101, A-1040 Wien
- Ernst Karner
- Vienna University of Technology, Institute for Analysis and Scientific Computing, Wiedner Hauptstrasse 8-10/101, A-1040 Wien
- Othmar Koch
- Vienna University of Technology, Institute for Analysis and Scientific Computing, Wiedner Hauptstrasse 8-10/101, A-1040 Wien
- Ewa Weinmüller
- Vienna University of Technology, Institute for Analysis and Scientific Computing, Wiedner Hauptstrasse 8-10/101, A-1040 Wien
- Received: 2005-10-25.
