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

P. Lima, L. Morgado

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.




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

Article Metrics

Metrics Loading ...

Metrics powered by PLOS ALM

Refbacks

  • There are currently no refbacks.



Trends in Computational and Applied Mathematics

A publication of the Brazilian Society of Applied and Computational Mathematics (SBMAC)

 

Indexed in:

                       

 

Desenvolvido por:

Logomarca da Lepidus Tecnologia