Abstract
We investigate analytical and numerical properties of systems of linear ordinary differential equations 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 guaranteeing existence and uniqueness of solutions which are continuous on a closed interval including the singular point t = 0. Moreover, we study the convergence behaviour of collocation schemes applied to solve the problem numerically.
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