The discrete minimum principle for quadratic spline discretization of a singularly perturbed problem

Abstract

We consider a singularly perturbed boundary value problem with two small parameters. The problem is numerically treated by a quadratic spline collocation method. The suitable choice of collocation points provides the discrete minimum principle. Error bounds for the numerical approximations are established. Numerical results give justification of the parameter-uniform convergence of the numerical approximations. © 2009 IMACS.