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I. Rachunkova, S. Stanek, J. Vampolova, E. Weinmüller:
"On linear ODEs with a time singularity of the first kind and unsmooth inhomogeneity.";
in: "ASC Report 07/2014", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2014, ISBN: 978-3-902627-07-0, 1 - 41.

In this paper we investigate analytical properties of systems of linear ordinary di fferential equations (ODEs) with unsmooth nonintegrable inhomogeneities and a time singularity of the first kind. We are especially interested in specifying the structure of general linear two-point boundary conditions guarantying existence
and uniqueness of solutions which are continuous on the closed interval including the singular point. Moreover, we study the convergence behaviour of collocation schemes applied to solve the problem numerically. Our theoretical results are supported by numerical experiments.

linear systems of ODEs; singular boundary value problem; time singularity of the rst kind; unsmooth inhomogeneity; existence and uniqueness; collocation method; convergence

http://www.asc.tuwien.ac.at/preprint/2014/asc07x2014.pdf