Asymptotic and Numerical Approximation of a Nonlinear Singular Boundary Value Problem

Autores

  • N.B. KONYUKHOVA
  • P.M. LIMA
  • M.P. CARPENTIER

DOI:

https://doi.org/10.5540/tema.2002.03.02.0141

Resumo

In this work, we consider a singular boundary value problem for a nonlinear second-order differential equation of the form g00(u) = ug(u)q=q; (0.1) where 0 < u < 1 and q is a known parameter, q < 0. We search for a positive solution of (0.1) which satisfies the boundary conditions g0(0) = 0; (0.2) lim u!1¡ g(u) = lim u!1¡ (1 ¡ u)g0(u) = 0: (0.3) We analyse the asymptotic properties of the solution of (0.1)-(0.3) near the singularity, depending on the value of q. We show the existence of a one-parameter family of solutions of equation (0.1) which satisfy the boundary condition (0.3) and obtain convergent or asymptotic expansions of these solutions.

Referências

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Publicado

2002-06-01

Como Citar

KONYUKHOVA, N., LIMA, P., & CARPENTIER, M. (2002). Asymptotic and Numerical Approximation of a Nonlinear Singular Boundary Value Problem. Trends in Computational and Applied Mathematics, 3(2), 141–150. https://doi.org/10.5540/tema.2002.03.02.0141

Edição

v. 3 n. 2 (2002)

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Artigo Original

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