Modified Successive Overrelaxation (MSOR) and Equivalent 2-Step Iterative Methods for Collocation Matrices

Abstract

We consider a class of consistently ordered matrices which arise from the discretization of Boundary Value Problems (BVPs) when the finite element collocation method, with Hermite elements, is used. Through a recently derived equivalence relationship for the asymptotic rates of convergence of the Modified Successive Overrelaxation (MSOR) and a certain 2-step iterative method, we determine the optimum values for the parameters of the MSOR method, as it pertains to collocation matrices. A geometrical algorithm, which utilizes 'capturing ellipse' arguments, has been successfully used. The fast convergence properties of the optimum MSOR method are revealed after its comparison to several well-known iterative schemes. Numerical examples, which include the solution of Poisson's equation, are used to verify our results. '" Department of Mathematics, University of Ioannina, GR-451 10 Ioannina, Greece. Visiting, Department of Computer Sciences, Purdue University, West Lafayeue, IN 47907. The work of this author was supported in part by AFOSR grant 88/0243 and by NSF grant CCR-8619817. *'" Department of Mathematics and Computer Science, Clarkson UniversilY, Potsdam, NY 13676

Extracted Key Phrases

6 Figures and Tables

Cite this paper

@inproceedings{Hadjidimos2013ModifiedSO, title={Modified Successive Overrelaxation (MSOR) and Equivalent 2-Step Iterative Methods for Collocation Matrices}, author={Apostolos Hadjidimos and Yiannis G. Saridakis}, year={2013} }