P-Cyclic SOR for BVPs with periodic boundary conditionsP-Cyclic SOR for BVPs with periodic boundary conditions Peer-Reviewed Journal Publication Δημοσίευση σε Περιοδικό με Κριτές 2015-10-162010enThe employment of finite element or finite difference discretization schemes, for the numerical solution of Boundary Value Problems (BVPs) with periodic type Boundary Conditions (BCs), leads to a large and sparse linear system whose coefficient matrix is in normal p-cyclic form. The use of block iterative methods, for the solution of such linear systems, and the demand for fast convergence rates, require the optimal repartitioning of the coefficient matrix. In this work, we make use of the finite element Hermite collocation method to discretize the BVP and the SOR iterative method to solve the corresponding sparse linear system. The optimal repartitioning of the collocation coefficient matrix leads to SOR methods with optimal rates of convergence.http://creativecommons.org/licenses/by/4.0/Applied Numerical Mathematics460411–419 Saridakis Ioannis Σαριδακης Ιωαννης Papadopoulou Eleni Παπαδοπουλου Ελενη Papadomanolaki, Maria Elsevier Greek mathematics mathematics greek greek mathematics