C¹-APPROXIMATE SOLUTIONS OF SECOND-ORDER SINGULAR ORDINARY DIFFERENTIAL EQUATIONS.

In this work a new method is developed to obtain C1-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. [ABSTRACT FROM AUTHOR]