Sains
Malaysiana 38(5)(2009): 729–733
An Accelerated Over-Relaxation
Quarter-Sweep Point Iterative Method for
Two-Dimensional Poisson
Equation
(Kaedah
Lelaran Titik Suku Sapuan Pengenduran Berlebihan Terpecut bagi Persamaan Poisson 2-Matra)
Shukhrat I. Rakhimov*
Institute for Mathematical
Research, Universiti Putra Malaysia
43400 UPM Serdang, Selangor D.E., Malaysia
Mohamed Othman
Dept of Communication Tech and
Network
Faculty of Computer Science
and Information Technology, Universiti Putra Malaysia
43400 UPM Serdang, Selangor D.E., Malaysia
Diserahkan: 11 September 2008
/ Diterima: 12 Mac 2009
ABSTRACT
Iterative
methods, particularly over-relaxation methods, are efficiently and frequently
used to solve large systems oflinear equations, because in the solutions of
partial differential equations, these methods are applied to systems which are
resulted from different iterative schemes to discrete equations. In this paper
we formulate an accelerated over-relaxation (AOR) method with the quarter-sweep iterative scheme applied to the
Poisson equation. To benchmark the new method we conducted experiments by
comparing it with the previous AOR methods based on full- and half-sweep iterative schemes. The
results of the experiments and the estimation of the computational complexity
of the methods proved the superiority of the new method.
Keywords:
Accelerated over-relaxation; point iterative methods; Poisson equation
ABSTRAK
Kaedah
lelaran, khususnya kaedah pengenduran berlebihan, kerap digunakan secara cekap
bagi menyelesaikan sistem persaman linear yang besar, kerana dalam penyelesaian
persamaan pembezaan separa, kaedah lelaran ini digunakan ke atas sistem yang
terhasil daripada skema lelaran berbeza untuk mengdiskretkan persamaan. Dalam
kertas kerja ini, kami memformulasikan kaedah pengenduran berlebihan tercepat (PBT) dengan menggunakan pendekatan sapuan suku dan mengaplikasikannya
kepada sistem persamaan Poisson. Sebagai penanda aras kaedah terbaru ini, kami melakukan beberapa kajian dan membandingkan dengan
kaedah PBT terdahulu yang menggunakan
pendekatan lelaran sapuan penuh dan separuh. Hasil ujikaji
tersebut dan anggaran pengiraan kekompleksitian bagi semua kaedah tersebut
telah membuktikan keberkesanan kaedah baru ini.
Kata kunci:
Kaedah lelaran titik; pengenduran berlebihan terpecut; persamaan Poisson
RUJUKAN
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*Pengarang untuk surat-menyurat;
email: sh.rakhimov@gmail.com
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