P. Lima, L. Morgado, M. Schöbinger, E. Weinmüller:

"A novel Computational Approach to Singular Free Boundary Problems in Ordinary Differential Equations";

in: "ASC Report 11/2016", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2016, 1 - 13.

We study the numerical solution of a singular free boundary problem for a second order nonlinear ordinary diﬀerential equation, where the diﬀerential operator is the degenerate m-Laplacian. A typical diﬃculty arising in free boundary problems is that the analytical solution may become non-smooth at one bound-ary or at both boundaries of the interval of integration. A numerical method proposed in [18] consists of two steps. First, a smoothing variable transformation is applied to the analytical problem in order to im-prove the smoothness of its solution. Then, the problem is discretized by means of a ﬁnite diﬀerence scheme.

Degenerate Laplacian, singular free boundary problem, smoothing variable substitution, collocation methods.

http://www.asc.tuwien.ac.at/preprint/2016/asc11x2016.pdf

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