On collocation methods for singular perturbation problems of convection-diffusion type


Katarina Surla, Ljiljana Teofanov, Zorica Uzelac




A collocation method using cubic spline for second-order linear singularly-perturbed two-point boundary value problem of convection-diffusion type is developed. The approximate solution is determined by collocation at the nodes 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 example comparing the methods is presented.