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Asymptotic expansions and numerical approximation of nonlinear degenerate boundary-value problems

✍ Scribed by P.M. Lima; M.P. Carpentier

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
163 KB
Volume
30
Category
Article
ISSN
0168-9274

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✦ Synopsis

In the present paper we are concerned with boundary-value problems (BVP) for the generalized Emden-Fowler equations. Asymptotic expansions of the solution are obtained near the endpoints. We use a finite-difference scheme to approximate the solution and the convergence is accelerated by means of extrapolation methods. A variable substitution is introduced to diminish the effect of the singularity at the origin. Numerical results, obtained by different methods, are presented for two particular cases.

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## Abstract In this paper, we obtain a sequence of approximate solution converging uniformly to the exact solution of a class of fourth‐order nonlinear boundary value problems. Its exact solution is represented in the form of series in the reproducing kernel space. The __n__‐term approximation __u_