Finite difference solution of a singular boundary value problem for the p-Laplace operator

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• 作者：M. Lu¨ªsa Morgado and Pedro Miguel Lima
• 关键词：Singular boundary value problem ; Ordinary differential equation ; p ; Laplacian ; Upper and lower solutions ; Finite difference method ; Variable substitution
• 刊名：Numerical Algorithms
• 出版年：2010
• 出版时间：November 2010
• 年：2010
• 卷：55
• 期：2-3
• 页码：337-348
• 全文大小：288.2 KB

文摘

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.