Analysis and Numerical Approximation of a Free Boundary Problem for a Singular Ordinary Differential Equation

Authors

  • P. Lima
  • L. Morgado

DOI:

https://doi.org/10.5540/tema.2007.08.02.0259

Abstract

We analyse a free boundary problem for a second order nonlinear or-dinary differential equation. The asymptotic behavior of the solutions satisfyingcertain boundary conditions is analysed at the endpoints of the interval where thesolution is sought. Based on this study, an efficient shooting method is introducedand numerical results are obtained.

References

[1] B. Franchi, E. lanconelli, J. Serrin, Existence and uniqueness of nonnegative solutions of quasilinear equations in Rn, Advances in Math., 118 (1996), 177-243.

H.G. Kaper, M.K. Kwong, Free boundary problems for Emden-Fowler equations, Diff. Int. Eqs, 3 (1990), 353-362.

N.B. Konyukhova, Singular Cauchy problems for systems of ordinary differential equations, USSR Comput. Maths. Math. Phys., 23 (1983), 72-82.

P.M. Lima, N.B. Konyukhova, A.I. Sukov, N.V. Chemetov, Analytical–Numerical Investigation of Bubble–Type Solutions of Nonlinear Singular Problems, J. Comput. Appl. Math., 189 (2006), 260-273.

P. Lima, L. Morgado, Numerical approximation of singular boundary value problems for a nonlinear differential equation, submited to the Proceedings of Equadiff 11, 2005.

G. Miller, V. Faber, A.B. White Jr., Finding plasma equilibria with magnetic islands, J. Computation Physics, 79 (1998), 417-435.

Downloads

Published

2007-08-13

How to Cite

Lima, P., & Morgado, L. (2007). Analysis and Numerical Approximation of a Free Boundary Problem for a Singular Ordinary Differential Equation. Trends in Computational and Applied Mathematics, 8(2), 259–268. https://doi.org/10.5540/tema.2007.08.02.0259

Issue

Vol. 8 No. 2 (2007)

Section

Original Article

License

Authors who publish in this journal agree to the following terms: 

  1. Authors retain copyright and grant the journal the right of first publication, with the work simultaneously licensed under the Creative Commons Attribution License that allows the sharing of the work with acknowledgment of authorship and initial publication in this journal.

  2. Authors are authorized to assume additional contracts separately, for non-exclusive distribution of the version of the work published in this journal (eg, publish in an institutional repository or as a book chapter), with acknowledgment of authorship and initial publication in this journal.
     

  3. Authors are allowed and encouraged to publish and distribute their work online (eg, in institutional repositories or on their personal page) at any point before or during the editorial process, as this can generate productive changes as well as increase impact and the citation of the published work (See The effect of open access).

  4. This is an open access journal which means that all content is freely available without charge to the user or his/her institution. Users are allowed to read, download, copy, distribute, print, search, or link to the full texts of the articles, or use them for any other lawful purpose, without asking prior permission from the publisher or the
    author. This is in accordance with the BOAI definition of open access

 

Intellectual Property

All the contents of this journal, except where otherwise noted, is licensed under a Creative Commons Attribution License under attribution BY.