A numerical algorithm for singular perturbation problems exhibiting weak boundary layers

A class of singularly perturbed two-point boundary-value problems (BVP) for second-order ordinary differential equations is considered here. To avoid the numerical difficulties in the solution to these problems, we divide the domain into two subdomains. The first BVP is a layer domain problem and the second BVP is a regular domain problem. Error estimates are derived for the numerical solution. Numerical examples are provided in support of the proposed method.