Efficacy of variational iteration method for chaotic Genesio system - Classical and multistage approach

Research output: Contribution to journalArticle

26 Citations (Scopus)

Abstract

This is a case study of solving the Genesio system by using the classical variational iteration method (VIM) and a newly modified version called the multistage VIM (MVIM). VIM is an analytical technique that grants us a continuous representation of the approximate solution, which allows better information of the solution over the time interval. Unlike its counterpart, numerical techniques, such as the Runge-Kutta method, provide solutions only at two ends of the time interval (with condition that the selected time interval is adequately small for convergence). Furthermore, it offers approximate solutions in a discretized form, making it complicated in achieving a continuous representation. The explicit solutions through VIM and MVIM are compared with the numerical analysis of the fourth-order Runge-Kutta method (RK4). VIM had been successfully applied to linear and nonlinear systems of non-chaotic in nature and this had been testified by numerous scientists lately. Our intention is to determine whether VIM is also a feasible method in solving a chaotic system like Genesio. At the same time, MVIM will be applied to gauge its accuracy compared to VIM and RK4. Since, for most situations, the validity domain of the solutions is often an issue, we will consider a reasonably large time frame in our work.

Original languageEnglish
Pages (from-to)2152-2159
Number of pages8
JournalChaos, Solitons and Fractals
Volume40
Issue number5
DOIs
Publication statusPublished - 15 Jun 2009

Fingerprint

Variational Iteration Method
Chaotic System
Efficacy
Runge-Kutta Methods
Interval
Approximate Solution
Numerical Techniques
Explicit Solution
Fourth Order
Numerical Analysis
Gauge
Nonlinear Systems
Linear Systems

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

@article{f91dac83ba674b18ba729da0fe557289,
title = "Efficacy of variational iteration method for chaotic Genesio system - Classical and multistage approach",
abstract = "This is a case study of solving the Genesio system by using the classical variational iteration method (VIM) and a newly modified version called the multistage VIM (MVIM). VIM is an analytical technique that grants us a continuous representation of the approximate solution, which allows better information of the solution over the time interval. Unlike its counterpart, numerical techniques, such as the Runge-Kutta method, provide solutions only at two ends of the time interval (with condition that the selected time interval is adequately small for convergence). Furthermore, it offers approximate solutions in a discretized form, making it complicated in achieving a continuous representation. The explicit solutions through VIM and MVIM are compared with the numerical analysis of the fourth-order Runge-Kutta method (RK4). VIM had been successfully applied to linear and nonlinear systems of non-chaotic in nature and this had been testified by numerous scientists lately. Our intention is to determine whether VIM is also a feasible method in solving a chaotic system like Genesio. At the same time, MVIM will be applied to gauge its accuracy compared to VIM and RK4. Since, for most situations, the validity domain of the solutions is often an issue, we will consider a reasonably large time frame in our work.",
author = "Goh, {S. M.} and {Md. Noorani}, {Mohd. Salmi} and Ishak Hashim",
year = "2009",
month = "6",
day = "15",
doi = "10.1016/j.chaos.2007.10.003",
language = "English",
volume = "40",
pages = "2152--2159",
journal = "Chaos, Solitons and Fractals",
issn = "0960-0779",
publisher = "Elsevier Limited",
number = "5",

}

TY - JOUR

T1 - Efficacy of variational iteration method for chaotic Genesio system - Classical and multistage approach

AU - Goh, S. M.

AU - Md. Noorani, Mohd. Salmi

AU - Hashim, Ishak

PY - 2009/6/15

Y1 - 2009/6/15

N2 - This is a case study of solving the Genesio system by using the classical variational iteration method (VIM) and a newly modified version called the multistage VIM (MVIM). VIM is an analytical technique that grants us a continuous representation of the approximate solution, which allows better information of the solution over the time interval. Unlike its counterpart, numerical techniques, such as the Runge-Kutta method, provide solutions only at two ends of the time interval (with condition that the selected time interval is adequately small for convergence). Furthermore, it offers approximate solutions in a discretized form, making it complicated in achieving a continuous representation. The explicit solutions through VIM and MVIM are compared with the numerical analysis of the fourth-order Runge-Kutta method (RK4). VIM had been successfully applied to linear and nonlinear systems of non-chaotic in nature and this had been testified by numerous scientists lately. Our intention is to determine whether VIM is also a feasible method in solving a chaotic system like Genesio. At the same time, MVIM will be applied to gauge its accuracy compared to VIM and RK4. Since, for most situations, the validity domain of the solutions is often an issue, we will consider a reasonably large time frame in our work.

AB - This is a case study of solving the Genesio system by using the classical variational iteration method (VIM) and a newly modified version called the multistage VIM (MVIM). VIM is an analytical technique that grants us a continuous representation of the approximate solution, which allows better information of the solution over the time interval. Unlike its counterpart, numerical techniques, such as the Runge-Kutta method, provide solutions only at two ends of the time interval (with condition that the selected time interval is adequately small for convergence). Furthermore, it offers approximate solutions in a discretized form, making it complicated in achieving a continuous representation. The explicit solutions through VIM and MVIM are compared with the numerical analysis of the fourth-order Runge-Kutta method (RK4). VIM had been successfully applied to linear and nonlinear systems of non-chaotic in nature and this had been testified by numerous scientists lately. Our intention is to determine whether VIM is also a feasible method in solving a chaotic system like Genesio. At the same time, MVIM will be applied to gauge its accuracy compared to VIM and RK4. Since, for most situations, the validity domain of the solutions is often an issue, we will consider a reasonably large time frame in our work.

UR - http://www.scopus.com/inward/record.url?scp=65549135923&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=65549135923&partnerID=8YFLogxK

U2 - 10.1016/j.chaos.2007.10.003

DO - 10.1016/j.chaos.2007.10.003

M3 - Article

VL - 40

SP - 2152

EP - 2159

JO - Chaos, Solitons and Fractals

JF - Chaos, Solitons and Fractals

SN - 0960-0779

IS - 5

ER -