Singular boundary value problems for ODEs, PDEs and DAEs arise often in applications and this explains great interest in their numerical solution. The difficulty here is the in general the right-hand side of such systems is not Lipschitz continuous and therefore the classical tools for the analysis and the convergence theory are not applicable. We discuss how the classical techniques need to be modified in order to become suitable for singular problems. Each participant gives a seminar talk about a particular topic on the basis of specified literature, in cooperation with his personal advisor

We begin with the existence and uniqueness theory for the continuous solutions of the analytical problems. Moreover, we discuss their smoothness properties. Next we deal with the convergence theory for the finite difference schemes and collocation methods. Also, we discuss the solvability of singular DAEs and the convergence of the collocation schemes applied for their numerical solution - an actual research area in the Research Group Numerics and Simulation of Differential Equations of our institute. Finally, we discuss results of numerical simulations for certain applications. Necessary technical tools: Fixed Point Theorems and the concept of stability for operator equations developed by H. Keller - the founder of the BVPs theory.

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