Liouville-Green Transform Method for Linear Singular Perturbation Boundary Value Problems

The numerical treatment of singular perturbation problems is currently a field in which active research is going on these days. Singular perturbation problems in which the term containing the highest order derivative is multiplied by a small parameter epsilon, occur in a number of areas of applied mathematics, science and engineering, among them fluid mechanics (boundary layer problems), elasticity (edge effect in shells) and quantum mechanics. In this paper, a linear singularly perturbed two-point boundary value problem with the boundary layer at left end point is solved. The given singularly perturbed two-point boundary value problem is replaced by Liouville-Green transform method. This transformed problem is solved. One linear numerical example has been solved to demonstrate the applicability of the method.