Sains Malaysiana 42(3)(2013): 347–358

A Step Variational Iteration Method for Solving Non-Chaotic and Chaotic Systems

(Kaedah Lelaran Ubahan Langkah bagi Menyelesaikan Sistem Kalut dan Tak Kalut)

R. Yulita Molliq* *

Department of Mathematics, Faculty of Mathematics and Natural Science, Universitas Negeri Medan

20221 Medan, Sumatera Utara, Indonesia

M.S.M. Noorani & R.R. Ahmad

School of Mathematical Sciences, Faculty of Science and Technology

Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor D.E. Malaysia

A.K. Alomari

Department of Mathematics, Faculty of Science, Hashemite University 13115 Zarqa, Jordan

Diserahkan: 25 Mei 2010/Diterima: 17 September 2012

ABSTRACT

In this paper, a new reliable method called the step variational iteration method (SVIM) based on an adaptation of the variational iteration method (VIM) is presented to solve non–chaotic and chaotic systems. The SVIM uses the general Lagrange multipliers for constructing the correction functional for the problems. The SVIM yields a step analytical solution of the form of a rapidly convergent infinite power series with easily computable terms and obtain a good approximate solution for larger intervals. The accuracy of the presented solution obtained is in an excellent agreement with the previously published solutions.

Keywords: Chaotic and non-chaotic systems; Lagrange multiplier; multistage variational iteration method; step variational iteration method; variational iteration method

ABSTRAK

Dalam kertas ini, kaedah baru dinamakan kaedah lelaran ubahan langkah (KLUL) berasaskan satu adaptasi kaedah lelaran ubahan digunakan untuk sistem tak-kalut dan kalut. KLUL menggunakan pendarab Lagrange umum untuk membina fungsian pembetulan bagi mengatasi masalah berkenaan. KLUL menghasilkan penyelesaian analisis dalam bentuk siri kuasa tak terhingga yang menumpu pantas dengan sebutan yang mudah dikira. Penyelesaian penghampiran diperoleh adalah baik untuk selang yang lebih besar. Ketepatan penyelesaian yang diperoleh adalah sangat baik bila dibandingkan dengan penyelesaian yang terdahulu.

Kata kunci: Kaedah lelaran ubahan; kaedah lelaran ubahan langkah; kaedah lelaran ubahan multitahap; sistem tak-kalut dan kalut; pendarab Lagrange

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*Pengarang untuk surat-menyurat; email: yulitamolliq@yahoo.com