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Faktor Pengenduran Optimum Masalah Nilai Sempadan Berkala Persamaan Pembeza Separa

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Author(s): Mohd Idris Jayes

Journal: Matematika
ISSN 0127-8274

Volume: 11;
Issue: 2;
Start page: 67;
Date: 1995;
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Keywords: Optimum relaxation factor | cyclic tridigonal square matrix | spectral radius | elliptic partial differential equation | periodic boundary conditions

ABSTRACT
The discretization of the second-order linear self-adjoint elliptic partial differential equation subject to periodic boundary conditions results in a system of linear equations of the form Mu = s, where M is block cyclic tridigonal square matrix. In Mohd Idris[1] the relationship between the spectral radius and over-relaxation factor of the problem has been derived. In this paper, numerical experiment is conducted to show that the standart SOR formula is not applicable, although the optimum relaxation factor of both cases coincide asymptotically, that is, when the size of the problem is large. The optimization process of the realaxation factor for the periodic problem is also illustrated.
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