On the solutions of nonlinear differential equations

An approximate method for the solution of non-linear singularly perturbed problems for second order ordinary differential equations with a boundary layer is studied. The region is divided into two parts as inner and outer region. The original second order singularly perturbed problem is replaced by an asymptotically equivalent first order problem and solved in the inner and outer regions. Then, the solutions of inner and outer region problems are matched to obtain an approximate uniform solution to the original problem.