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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 Received: 28 October
2015/Accepted: 23 March 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 REFERENCES Awoyemi,
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