On the Solution of Singularly Perturbed Equations Using Quintic Hermite Collocation Scheme

The numerical solution to singularly perturbed two-point boundary value problems with a boundary layer at end points is provided in this study using a Hermite collocation numerical approach with quintic basis. The Hermite collocation strategy reduces the proposed problem to an algebraic system of equations. Four different problems have been investigated for varying singular perturbation parameter \(\epsilon \) through which the scheme’s applicability and computational impact have been explored. To assess the stability, \(L_{2},L_{\infty }\) and the root mean square error have been determined. The comparison have been shown in Exact and numerical values along with absolute error which agrees upto a good level of accuracy. The results have been interpreted in tabular and graphical form.