Contributions to Books:

J. Burkotova, I. Rachunkova, E. Weinmüller:
"On singular BVPs with unsmooth data. Part 2: Convergence of the collocation schemes";
in: "ASC Report 30/2017", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2017, ISBN: 978-3-902627-10-0, 1 - 23.

English abstract:
This paper deals with the collocation method applied to solve systems of singular linear ordinary differential equations with variable coefficient matrices and unsmooth inhomogeneities. The classical stage convergence order is shown to hold for the piecewise polynomial collocation applied to boundary value problems with time singularities of the first kind provided that their solutions are appropriately smooth. The question of the existence and uniqueness of solutions to the analytical problems have been investigated in the first part of the paper - On singular BVPs with unsmooth data. Part1: Analysis of the linear case with variable coefficient matrix. The convergence theory is illustrated by numerical examples.

linear systems of ordinary differential equations singular boundary value problems time singularity of the first kind unsmooth inhomogeneity collocation method convergence

Electronic version of the publication:

Created from the Publication Database of the Vienna University of Technology.