Integration for special third-order ordinary differential equations using improved Runge-Kutta direct method

Kasim Abbas Hussain; Fudziah Ismail; Norazak Senu; Faranak Rabiei; Rabha Ibrahim

doi:10.22452/mjs.vol34no2.4

Integration for special third-order ordinary differential equations using improved Runge-Kutta direct method

Kasim Abbas Hussain, Fudziah Ismail, Norazak Senu, Faranak Rabiei, Rabha Ibrahim

Research output: Contribution to journal › Article › Research › peer-review

8 Citations (Scopus)

Abstract

In this paper, we derive an explicit four stage fifth-order Improved Runge-Kutta (IRKD) method for numerical integration of special third-order ordinary differential equation. The method proposed here is two-step in nature and require less number of stages per step compared with the existing Runge-Kutta (RK) method. The stability polynomial of the IRKD method is presented. Numerical results are given to illustrate the efficiency of the proposed method compared to the RK method and direct Runge-Kutta (RKD) method for solving special third-order ordinary differential equations.

Original language	English
Pages (from-to)	172-179
Number of pages	8
Journal	Malaysian Journal of Science
Volume	34
Issue number	2
DOIs	https://doi.org/10.22452/mjs.vol34no2.4
Publication status	Published - 2015
Externally published	Yes

Keywords

IRKD method
Runge-Kutta method
Special third-order ordinary differential equations
Stability Ploynomial

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10.22452/mjs.vol34no2.4

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title = "Integration for special third-order ordinary differential equations using improved Runge-Kutta direct method",

abstract = "In this paper, we derive an explicit four stage fifth-order Improved Runge-Kutta (IRKD) method for numerical integration of special third-order ordinary differential equation. The method proposed here is two-step in nature and require less number of stages per step compared with the existing Runge-Kutta (RK) method. The stability polynomial of the IRKD method is presented. Numerical results are given to illustrate the efficiency of the proposed method compared to the RK method and direct Runge-Kutta (RKD) method for solving special third-order ordinary differential equations.",

keywords = "IRKD method, Runge-Kutta method, Special third-order ordinary differential equations, Stability Ploynomial",

author = "Hussain, \{Kasim Abbas\} and Fudziah Ismail and Norazak Senu and Faranak Rabiei and Rabha Ibrahim",

year = "2015",

doi = "10.22452/mjs.vol34no2.4",

language = "English",

volume = "34",

pages = "172--179",

journal = "Malaysian Journal of Science",

issn = "1394-3065",

publisher = "University of Malaya",

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TY - JOUR

T1 - Integration for special third-order ordinary differential equations using improved Runge-Kutta direct method

AU - Hussain, Kasim Abbas

AU - Ismail, Fudziah

AU - Senu, Norazak

AU - Rabiei, Faranak

AU - Ibrahim, Rabha

PY - 2015

Y1 - 2015

N2 - In this paper, we derive an explicit four stage fifth-order Improved Runge-Kutta (IRKD) method for numerical integration of special third-order ordinary differential equation. The method proposed here is two-step in nature and require less number of stages per step compared with the existing Runge-Kutta (RK) method. The stability polynomial of the IRKD method is presented. Numerical results are given to illustrate the efficiency of the proposed method compared to the RK method and direct Runge-Kutta (RKD) method for solving special third-order ordinary differential equations.

AB - In this paper, we derive an explicit four stage fifth-order Improved Runge-Kutta (IRKD) method for numerical integration of special third-order ordinary differential equation. The method proposed here is two-step in nature and require less number of stages per step compared with the existing Runge-Kutta (RK) method. The stability polynomial of the IRKD method is presented. Numerical results are given to illustrate the efficiency of the proposed method compared to the RK method and direct Runge-Kutta (RKD) method for solving special third-order ordinary differential equations.

KW - IRKD method

KW - Runge-Kutta method

KW - Special third-order ordinary differential equations

KW - Stability Ploynomial

UR - http://www.scopus.com/inward/record.url?scp=85019692484&partnerID=8YFLogxK

U2 - 10.22452/mjs.vol34no2.4

DO - 10.22452/mjs.vol34no2.4

M3 - Article

AN - SCOPUS:85019692484

SN - 1394-3065

VL - 34

SP - 172

EP - 179

JO - Malaysian Journal of Science

JF - Malaysian Journal of Science

IS - 2

ER -

Integration for special third-order ordinary differential equations using improved Runge-Kutta direct method

Abstract

Keywords

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