A novel computational approach to singular free boundary problems in ordinary differential equations
| Autor: | Ewa Weinmüller, Pedro M. Lima, M. Schöbinger, M. L. Morgado |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Numerical Analysis
Applied Mathematics 010102 general mathematics Mathematical analysis Mixed boundary condition Singular boundary method 01 natural sciences Elliptic boundary value problem 010101 applied mathematics Computational Mathematics Singular solution Collocation method Ordinary differential equation Free boundary problem Boundary value problem 0101 mathematics Mathematics |
| Zdroj: | Applied Numerical Mathematics. 114:97-107 |
| ISSN: | 0168-9274 |
| DOI: | 10.1016/j.apnum.2016.09.017 |
| Popis: | 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 boundary 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 improve 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 bvpsuite17 can be successfully applied for its numerical approximation. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full Text from ScienceDirect