TY  - JOUR
ID  - Auzinger2006
LB  - Auzinger2006
AU  - Auzinger, Winfried
AU  - Karner, Ernst
AU  - Koch, Othmar
AU  - Weinmüller, Ewa
TI  - Collocation methods for the solution of eigenvalue problems for singular ordinary differential equations
ST  - Collocation methods for the solution of eigenvalue problems for singular ordinary differential equations
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2006
VL  - 26
IS  - 2
SP  - 229
EP  - 241
DO  - http://dx.doi.org/10.7494/OpMath.2006.26.2.229
UR  - http://dx.doi.org/10.7494/OpMath.2006.26.2.229
AB  - 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.
KW  - polynomial collocation
KW  - singular boundary value problems
KW  - linear and nonlinear eigenvalue problems
SN  - 1232-9274
ER  -