[Zurück]

W. Auzinger, O. Koch, E. Weinmüller:
"Efficient Collocation Schemes for Singular Boundary Value Problems";
Numerical Algorithms, 31 (2002), S. 5 - 25.

We discuss an error estimation procedure for the global error of collocation schemes applied to solve singular boundary value problems with a singularity of the first kind. This estimate of the global error was proposed by Stetter in 1978 and is based on the idea of Defect Correction, originally due to Zadunaisky. A carefully designed modification of this estimate presented here, not only results in less computational work but also proves robust with respect to the singularity. This estimate also provides a basis for a grid selection routine in which the grid is modified with the aim to equidistribute the global error. This procedure yields meshes suitable for an efficient numerical solution - most importantly, we observe that the grid is refined in a way reflecting only the behavior of the solution and remains unaffected by the unsmooth direction field close to the singular point.

http://dx.doi.org/10.1023/A:1021151821275

http://www.math.tuwien.ac.at/~ewa/PDF_Files/ecs_published.pdf