Electronic Journal of Differential Equations,
Vol. 2010(2010), No. 125, pp. 1-47.

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

Author: George L. Karakostas (Univ. of Ioannina, Greece)

Abstract:
 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 07, 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.