Modified successive overrelaxation (MSOR) and equivalent 2-step iterative methods for collocation matricesModified successive overrelaxation (MSOR) and equivalent 2-step iterative methods for collocation matrices Peer-Reviewed Journal Publication Δημοσίευση σε Περιοδικό με Κριτές 2015-10-161992enWe 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.http://creativecommons.org/licenses/by/4.0/Journal of Computational and Applied Mathematics342375–393 Saridakis Ioannis Σαριδακης Ιωαννης Hadjidimos, Apostolos Elsevier Greek mathematics mathematics greek greek mathematics --Cases, clinical reports, statistics --Statistical data statistics cases clinical reports statistics statistical data