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

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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.

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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

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