Abstract
We consider non-linear singular perturbation problems of the form
 y (x )  p(y (x ))y (x ) q(x , y (x ))  r (x ) , y (0)  , y (1)   with a boundary layer at one end point.
The method is distinguished by the following fact: The original problem is reduced to an
asymptotically equivalent first order initial value problem (IVP). Then, an initial-value
algorithm is applied to solve this IVP. The algorithm is based on the locally exact integration
of a linearized problem on a non-uniform mesh. Two terms recurrence relation with
controlled step size is obtained. Several problems are solved to demonstrate the applicability
and efficiency of the algorithm. It is observed that the present method approximates the exact
solution very well.