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Technical University of Crete
Technical University of Crete
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| URI: | http://purl.tuc.gr/dl/dias/136BC77B-7DAE-49C7-86EF-72EA897F4FDF | ||
| Year | 1992 | ||
| Type of Item | Peer-Reviewed Journal Publication | ||
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| Bibliographic Citation | A. Hadjidimos, Y. G. Saridakis, “Modified successive overrelaxation (MSOR) and equivalent 2-step iterative methods for collocation matrices," J. of Computaitonal and Applied Math ,vol.42, no.3, pp. 375-393, 1992. doi: 10.1016/0377-0427(92)90086-D https://doi.org/10.1016/0377-0427(92)90086-D | ||
| Appears in Collections |
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.
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