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Finite Difference Solution of a Singular Boundary Value Problem for the P-Laplace Operator

Morgado, M. Luísa; Lima, Pedro M.

Numerical Algorithms, 55(2-3) (2010), 337-348

We are concerned about a singular boundary value problem for a second order nonlinear ordinary differential equation. The differential operator of this equation is the radial part of the so-called N-dimensional p-Laplacian (where p?>?1), which reduces to the classical Laplacian when p?=?2. We introduce a finite difference method to obtain a numerical solution and, in order to improve the accuracy of this method, we use a smoothing variable substitution that takes into account the behavior of the solution in the neighborhood of the singular points.