Document Type : Original Article

**Author**

**Abstract**

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.

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.

**Keywords**