P. Lima, L. Morgado, M. Schöbinger, E. Weinmüller:
"A Novel Computational Approach to Singular Free Boundary Problems in Ordinary Differential Equations";
Applied Numerical Mathematics,
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  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. In the present paper, we consider an alternative numerical approach. We first transform the original problem
into a special parameter dependent problem sometimes referred to as an `eigenvalue problem´. By applying a smoothing variable transformation to the resulting equation, we obtain a new problem whose solution is
smoother, and so the open domain Matlab collocation code bvpsuite
 can be successfully applied for its numerical approximation.
Degenerate Laplacian, singular free boundary problem, smoothing variable substitution, collocation methods
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