Electron. J. Diff. Equ., Vol. 2010(2010), No. 125, pp. 1-47.

C^1-approximate solutions of second-order singular ordinary differential equations

George L. Karakostas

In this work a new method is developed to obtain C^1-approximate solutions of initial and boundary-value problems generated from a one - parameter second order singular ordinary differential equation. Information about the order of approximation is also given by introducing the so called growth index of a function. Conditions are given for the existence of such approximations for initial and boundary-value problems of several kinds. Examples associated with the corresponding graphs of the approximate solutions, for some values of the parameter, are also given.

Submitted March 21, 2010. Published September 7, 2010.
Math Subject Classifications: 34A45, 34A12, 34A25, 34B99.
Key Words: One-parameter second order ordinary differential equation; growth index of a function; Approximate solutions; Initial value problems; boundary value problems.

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George L. Karakostas
Department of Mathematics, University of Ioannina
451 10 Ioannina, Greece
email: gkarako@uoi.gr

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