Sains Malaysiana 39(4)(2010): 639–646
Kaedah Pasangan 4(3)
Runge-Kutta-Nystršm untuk Masalah Nilai Awal Berkala
(A
4(3) Pair Runge-Kutta-Nystršm Method for Periodic Initial Value Problems)
Norazak Senu*, Mohamed
Suleiman & Fudziah Ismail
Jabatan Matematik, Fakulti
Sains, Universiti Putra Malaysia
43400 UPM Serdang, Selangor, Malaysia
Mohamed Othman
Jabatan Teknologi Komunikasi
dan Rangkaian
Fakulti Sains Komputer dan
Teknologi Maklumat
Universiti Putra Malaysia, 43400 UPM Serdang,
Selangor, Malaysia
Diserahkan: 14 Ogos 2009 / Diterima:
4 November 2009
ABSTRAK
Kaedah baru
pasangan benaman 4(3) tahap-empat berperingkat empat tak tersirat
Runge-Kutta-Nyström (RKN)
diterbitkan untuk mengamir persamaan pembezaan peringkat dua berbentuk yʺ =
f (x, y) dengan penyelesaian bentuk berkala. Dipersembahkan kaedah yang
bercirikan serakan berperingkat tinggi serta pekali ralat pangkasan utama yang
‘kecil’. Analisis kestabilan bagi kaedah yang diterbitkan juga diberikan.
Perbandingan keputusan berangka antara kaedah yang dihasilkan dengan kaedah
RK4(3) dan RKN4(3)D menunjukkan kaedah yang baru ini berkecekapan lebih baik
daripada segi penilaian fungsi dan masa pelaksanaan.
Kata kunci:
Kaedah Runge-Kutta-Nyström; penyelesaian berkala; serakan
ABSTRACT
A new
embedded 4(3) pair explicit four-stage fourth-order Runge-Kutta-Nyström (RKN) method was developed to integrate second-order differential
equations of the form yʺ = f (x, y) where the solution was oscillatory. Presented is
a method which has high order dispersion with a ‘small’ principal local
truncation error coefficient. The stability analysis of the method derived is
also given. Numerical comparisons of this new method with RK4(3) and RKN4(3)D
methods show its clear advantage in terms of function evaluations and
computation time.
Keywords:
Oscillatory solutions; Phase-lag; Runge-Kutta-Nyström methods
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*Pengarang untuk
surat-menyurat; email: razak@math.upm.edu.my
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