Solving Lorenz system by using Runge-Kutta method

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

In this study, the classical fourth-order Runge-Kutta method is modified to obtain new methods which are of order five. The methods are tested on the Lorenz system which involves the chaotic and nonchaotic characteristics. The modified fifth-order methods using arithmetic mean are compared with another method with the same order. Comparisons between the methods are made in two step sizes and the accuracy of all the methods are discussed. Mathematica and Matlab softwares are used to solve the Lorenz system and sketch the graphical solutions of the chaotic and non-chaotic system.

Original languageEnglish
Pages (from-to)241-251
Number of pages11
JournalEuropean Journal of Scientific Research
Volume32
Issue number2
Publication statusPublished - 2009

Fingerprint

Runge Kutta methods
Lorenz System
Runge-Kutta Methods
methodology
Mathematica
MATLAB
Fourth Order
method
Software
software

Keywords

  • Arithmetic Mean
  • Harmonic Mean
  • Lorenz System
  • Modified Fifth-Order Runge-Kutta Method

ASJC Scopus subject areas

  • General

Cite this

Solving Lorenz system by using Runge-Kutta method. / Razali, Noorhelyna; Ahmad, Rokiah @ Rozita.

In: European Journal of Scientific Research, Vol. 32, No. 2, 2009, p. 241-251.

Research output: Contribution to journalArticle

@article{8eca14609ce74245942a53bd64f23ce1,
title = "Solving Lorenz system by using Runge-Kutta method",
abstract = "In this study, the classical fourth-order Runge-Kutta method is modified to obtain new methods which are of order five. The methods are tested on the Lorenz system which involves the chaotic and nonchaotic characteristics. The modified fifth-order methods using arithmetic mean are compared with another method with the same order. Comparisons between the methods are made in two step sizes and the accuracy of all the methods are discussed. Mathematica and Matlab softwares are used to solve the Lorenz system and sketch the graphical solutions of the chaotic and non-chaotic system.",
keywords = "Arithmetic Mean, Harmonic Mean, Lorenz System, Modified Fifth-Order Runge-Kutta Method",
author = "Noorhelyna Razali and Ahmad, {Rokiah @ Rozita}",
year = "2009",
language = "English",
volume = "32",
pages = "241--251",
journal = "European Journal of Scientific Research",
issn = "1450-202X",
publisher = "European Journals Inc.",
number = "2",

}

TY - JOUR

T1 - Solving Lorenz system by using Runge-Kutta method

AU - Razali, Noorhelyna

AU - Ahmad, Rokiah @ Rozita

PY - 2009

Y1 - 2009

N2 - In this study, the classical fourth-order Runge-Kutta method is modified to obtain new methods which are of order five. The methods are tested on the Lorenz system which involves the chaotic and nonchaotic characteristics. The modified fifth-order methods using arithmetic mean are compared with another method with the same order. Comparisons between the methods are made in two step sizes and the accuracy of all the methods are discussed. Mathematica and Matlab softwares are used to solve the Lorenz system and sketch the graphical solutions of the chaotic and non-chaotic system.

AB - In this study, the classical fourth-order Runge-Kutta method is modified to obtain new methods which are of order five. The methods are tested on the Lorenz system which involves the chaotic and nonchaotic characteristics. The modified fifth-order methods using arithmetic mean are compared with another method with the same order. Comparisons between the methods are made in two step sizes and the accuracy of all the methods are discussed. Mathematica and Matlab softwares are used to solve the Lorenz system and sketch the graphical solutions of the chaotic and non-chaotic system.

KW - Arithmetic Mean

KW - Harmonic Mean

KW - Lorenz System

KW - Modified Fifth-Order Runge-Kutta Method

UR - http://www.scopus.com/inward/record.url?scp=67649855155&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=67649855155&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:67649855155

VL - 32

SP - 241

EP - 251

JO - European Journal of Scientific Research

JF - European Journal of Scientific Research

SN - 1450-202X

IS - 2

ER -