ON THE FORMULATION AND IMPLEMENTATION OF OPTIMAL SUPERCONVERGENT ONE STEP QUADRATIC SPLINE COLLOCATION METHODS FOR ELLIPTIC PROBLEMS

Abstract. We formulate new optimal quadratic spline collocation methods for the solution of various elliptic boundary value problems in the unit square. These methods are constructed so that the collocation equations can be solved using a matrix decomposition algorithm. The results of numerical experiments exhibit the expected optimal global accuracy as well as superconvergence phenomena. AMS subject classifications. 65N35, 65N22. Key words. Elliptic boundary value problems, quadratic spline collocation, matrix decomposition algorithms, fast Fourier transforms, optimal convergence rates, superconvergence. 1. Introduction. C