Sains Malaysiana 44(3)(2015): 473–482

Zero-Dissipative Trigonometrically Fitted Hybrid Method for Numerical Solution of Oscillatory Problems

(Kaedah Hibrid Penyuaian Trigonometri Lesapan-Sifar untuk Penyelesaian Berangka Masalah Berayun)

YUSUF DAUDA JIKANTORO, FUDZIAH ISMAIL* & NORAZAK SENU

Department of Mathematics and Institute for Mathematical Research, Universiti Putra Malaysia

Serdang 43400, Selangor Darul Ehsan, Malaysia

Received: 7 January 2014/Accepted: 3 October 2014

ABSTRACT

In this paper, an improved trigonometrically fitted zero-dissipative explicit two-step hybrid method with fifth algebraic order is derived. The method is applied to several problems which solutions are oscillatory in nature. Numerical results obtained are compared with existing methods in the scientific literature. The comparison shows that the new method is more effective and efficient than the existing methods of the same order.

Keywords: Dispersion; hybrid method; oscillatory problems; oscillatory solution; trigonometrically fitted

ABSTRAK

Dalam kertas ini, suatu penyuaian trigonometri lesapan sifar kaedah hibrid dua langkah penambahbaikan peringkat kelima diterbitkan. Kaedah ini digunakan untuk beberapa masalah yang penyelesaiannya berayun. Keputusan berangka yang diperoleh dibandingkan dengan kaedah sedia ada dalam maklumat saintifik. Perbandingan tersebut menunjukkan kaedah yang yang baharu ini adalah lebih efektif dan cekap berbanding kaedah sedia ada dengan peringkat yang sama.

Kata kunci: Kaedah hibrid; masalah berayun; penyelesaian berayun; penyuaian trigonmetri; serakan

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*Corresponding author; email: fudziah_i@yahoo.com.my