Sains Malaysiana 47(11)(2018): 2927–2932

http://dx.doi.org/10.17576/jsm-2018-4711-36

 

Comparison of One-Step and Two-Step Symmetrization in the Variable Stepsize Setting

(Perbandingan Satu dan Dua Langkah Pensimetrian dalam Persekitaran Saiz Langkah Berubah-Ubah)

 

N. RAZALI^*, Z.M. NOPIAH & H. OTHMAN

 

Centre of Research in Engineering Education and Built Environment, Program of Fundamental Engineering Studies, Faculty of Engineering and Built Environment, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor Darul Ehsan, Malaysia

 

Diserahkan: 15 November 2017/Diterima: 22 Mei 2018

 

ABSTRACT

In this paper, we study the effects of symmetrization by the implicit midpoint rule (IMR) and the implicit trapezoidal rule (ITR) on the numerical solution of ordinary differential equations. We extend the study of the well-known formula of Gragg to a two-step symmetrizer and compare the efficiency of their use with the IMR and ITR. We present the experimental results on nonlinear problem using variable stepsize setting and the results show greater efficiency of the two-step symmetrizers over the one-step symmetrizers of IMR and ITR.

 

Keywords: Implicit midpoint rule; implicit trapezoidal rule; symmetrizers

 

ABSTRAK

Dalam kertas ini, kami mengkaji kesan pensimetrian kaedah titik tengah tersirat (IMR) dan kaedah trapezium tersirat (ITR) ke atas penyelesaian berangka persamaan pembezaan biasa. Kami melanjutkan kajian terkenal oleh Gragg kepada pensimetri dua langkah dan membandingkan kecekapan penggunaannya dengan IMR dan ITR. Keputusan uji kaji pada masalah tidak linear menggunakan saiz langkah yang berubah-ubah menunjukkan bahawa pensimetri dua langkah adalah lebih cekap berbanding pensimetri satu langkah.

 

Kata kunci: Kaedah titik tengah tersirat; kaedah trapezium tersirat; pensimetri

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*Pengarang untuk surat-menyurat; email: helyna@ukm.edu.my