Asymptotic and Numerical Approximation of a Nonlinear Singular Boundary Value Problem

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

Abstract


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.

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

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Trends in Computational and Applied Mathematics

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