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Sains Malaysiana 45(11)(2016): 1747–1754
A Sixth-Order RKFD Method with Four-Stage for Directly Solving Special Fourth-Order
ODEs (Kaedah
RKFD Peringkat Keenam dengan Tahap
Empat untuk
Menyelesaikan Secara Terus PPB Khas Peringkat Keempat) FUDZIAH ISMAIL1,2*, KASIM HUSSAIN3
& NORAZAK SENU1,2 1Department of Mathematics,
Faculty of Science, Universiti Putra
Malaysia, 43400 Serdang, Selangor Darul
Ehsan, Malaysia 2Institute for Mathematical
Research, Universiti Putra Malaysia,
43400 Serdang, Selangor Darul Ehsan, Malaysia 3Department of Mathematics,
College of Science, Al-Mustansiriyah
University, Baghdad Iraq Diserahkan: 28 Oktober 2015/Diterima: 23 Mac 2016 ABSTRACT
In this article, the general
form of Runge-Kutta method for directly
solving a special fourth- order ordinary differential equations
denoted as RKFD
method is given. The order conditions up to order
seven are derived, based on the order conditions,
we construct a new explicit four-stage sixth-order RKFD method denoted as RKFD6
method. Zero-stability of the method is proven. Comparisons are
made using the existing Runge–Kutta
methods after the problems are reduced to a system of first order
ordinary differential equations. Numerical results are presented
to illustrate the efficiency and competency of the new method.
Keywords: Ordinary differential
equations; special fourth order; RKFD
method; Runge-Kutta method ABSTRAK
Dalam kertas ini,
bentuk umum kaedah
Runge-Kutta untuk
menyelesaikan secara terus persamaan pembezaan biasa khas peringkat keempat yang ditandakan sebagai kaedah RKFD diberikan. Syarat tertib
hingga ke
peringkat ketujuh diterbitkan, berasaskan syarat ini, kami bina kaedah baharu
RKFD
tahap empat
peringkat keenam yang ditandakan sebagai RKFD6.
Kestabilan
sifar kaedah
ini dibuktikan. Perbandingan dijalankan menggunakan kaedah Runge-Kutta sedia ada setelah
masalah tersebut
diturunkan kepada sistem persamaan pembezaan peringkat pertama. Keputusan berangka dipersembahkan
untuk menunjukkan
kecekapan dan kompetensi
kaedah yang baharu
tersebut. Kata kunci: Kaedah
RKFD; kaedah Runge-Kutta; peringkat keempat khas; persamaan
pembezaan biasa RUJUKAN Awoyemi, D.O.
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