On collocation methods for singular perturbation problems


Zorica Uzelac, Katarina Surla, Ljiljana Surla




A collocation method using cubic splines for second-order linear sigularly-perturbed two-point boundary value problem is developed. The approximate solution is determined by collocation at the points of a piecewise equidistant mesh of Shishkin type. We improve the method by changing the location of the collocation points from the mesh points to the Gauss-Legendre points. Numerical examples comparing the methods are presented.