Opuscula Mathematica

Opuscula Math.
 26
, no. 2
 (), 229-241
Opuscula Mathematica

Collocation methods for the solution of eigenvalue problems for singular ordinary differential equations





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.
Cite this article as:
Winfried Auzinger, Ernst Karner, Othmar Koch, Ewa Weinmüller, Collocation methods for the solution of eigenvalue problems for singular ordinary differential equations, Opuscula Math. 26, no. 2 (2006), 229-241
 
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ISSN 1232−9274, e-ISSN 2300−6919, DOI https://doi.org/10.7494/OpMath
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