Derivation of explicit 6(4) pair of hybrid methods for special second order ordinary differential equations

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Many physical problems can be modelled using special second order ordinary differential equations. Since someof the second order equations are either hard to be solved analytically or have no analytical solutions, therefore in the past research, there has been a continuous need for numerical methods for solving them. In this paper, the derivation of explicit 6(4) pair of hybrid methods with four stages is considered. For the higher order formula, the derivation is done by imposing the free parameter to increase the size of the interval of absolute stability. This method is implemented in variable step-size in which the lower order formula is used to approximate the local error. Numerical comparisons that have been carried out show that the new method outperforms the existing RungeKutta Nystrom 5(4) pair methodfor solving someoscillatory problems.

Original languageEnglish
Title of host publicationProceeding of the 25th National Symposium on Mathematical Sciences, SKSM 2017
Subtitle of host publicationMathematical Sciences as the Core of Intellectual Excellence
EditorsHamidah Maidinsah, Sarifah Radiah Sharif, Wan Eny Zarina Wan Abdul Rahman, Ajab Bai Akbarally, Mesliza Mohamed, Daud Mohamad, Maheran Mohd Jaffar
PublisherAmerican Institute of Physics Inc.
Volume1974
ISBN (Electronic)9780735416819
DOIs
Publication statusPublished - 28 Jun 2018
Event25th National Symposium on Mathematical Sciences: Mathematical Sciences as the Core of Intellectual Excellence, SKSM 2017 - Kuantan, Pahang, Malaysia
Duration: 27 Aug 201729 Aug 2017

Other

Other25th National Symposium on Mathematical Sciences: Mathematical Sciences as the Core of Intellectual Excellence, SKSM 2017
CountryMalaysia
CityKuantan, Pahang
Period27/8/1729/8/17

Fingerprint

differential equations
derivation
problem solving
intervals

Keywords

  • Sixth order hybrid method
  • Stability
  • Variable step-size

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Faieza, S., & Nor Farhah, R. (2018). Derivation of explicit 6(4) pair of hybrid methods for special second order ordinary differential equations. In H. Maidinsah, S. R. Sharif, W. E. Z. W. A. Rahman, A. B. Akbarally, M. Mohamed, D. Mohamad, & M. M. Jaffar (Eds.), Proceeding of the 25th National Symposium on Mathematical Sciences, SKSM 2017: Mathematical Sciences as the Core of Intellectual Excellence (Vol. 1974). [020077] American Institute of Physics Inc.. https://doi.org/10.1063/1.5041608

Derivation of explicit 6(4) pair of hybrid methods for special second order ordinary differential equations. / Faieza, Samat; Nor Farhah, Razak.

Proceeding of the 25th National Symposium on Mathematical Sciences, SKSM 2017: Mathematical Sciences as the Core of Intellectual Excellence. ed. / Hamidah Maidinsah; Sarifah Radiah Sharif; Wan Eny Zarina Wan Abdul Rahman; Ajab Bai Akbarally; Mesliza Mohamed; Daud Mohamad; Maheran Mohd Jaffar. Vol. 1974 American Institute of Physics Inc., 2018. 020077.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Faieza, S & Nor Farhah, R 2018, Derivation of explicit 6(4) pair of hybrid methods for special second order ordinary differential equations. in H Maidinsah, SR Sharif, WEZWA Rahman, AB Akbarally, M Mohamed, D Mohamad & MM Jaffar (eds), Proceeding of the 25th National Symposium on Mathematical Sciences, SKSM 2017: Mathematical Sciences as the Core of Intellectual Excellence. vol. 1974, 020077, American Institute of Physics Inc., 25th National Symposium on Mathematical Sciences: Mathematical Sciences as the Core of Intellectual Excellence, SKSM 2017, Kuantan, Pahang, Malaysia, 27/8/17. https://doi.org/10.1063/1.5041608
Faieza S, Nor Farhah R. Derivation of explicit 6(4) pair of hybrid methods for special second order ordinary differential equations. In Maidinsah H, Sharif SR, Rahman WEZWA, Akbarally AB, Mohamed M, Mohamad D, Jaffar MM, editors, Proceeding of the 25th National Symposium on Mathematical Sciences, SKSM 2017: Mathematical Sciences as the Core of Intellectual Excellence. Vol. 1974. American Institute of Physics Inc. 2018. 020077 https://doi.org/10.1063/1.5041608
Faieza, Samat ; Nor Farhah, Razak. / Derivation of explicit 6(4) pair of hybrid methods for special second order ordinary differential equations. Proceeding of the 25th National Symposium on Mathematical Sciences, SKSM 2017: Mathematical Sciences as the Core of Intellectual Excellence. editor / Hamidah Maidinsah ; Sarifah Radiah Sharif ; Wan Eny Zarina Wan Abdul Rahman ; Ajab Bai Akbarally ; Mesliza Mohamed ; Daud Mohamad ; Maheran Mohd Jaffar. Vol. 1974 American Institute of Physics Inc., 2018.
@inproceedings{2ab11940709f498eb7c15f6b7ec0053c,
title = "Derivation of explicit 6(4) pair of hybrid methods for special second order ordinary differential equations",
abstract = "Many physical problems can be modelled using special second order ordinary differential equations. Since someof the second order equations are either hard to be solved analytically or have no analytical solutions, therefore in the past research, there has been a continuous need for numerical methods for solving them. In this paper, the derivation of explicit 6(4) pair of hybrid methods with four stages is considered. For the higher order formula, the derivation is done by imposing the free parameter to increase the size of the interval of absolute stability. This method is implemented in variable step-size in which the lower order formula is used to approximate the local error. Numerical comparisons that have been carried out show that the new method outperforms the existing RungeKutta Nystrom 5(4) pair methodfor solving someoscillatory problems.",
keywords = "Sixth order hybrid method, Stability, Variable step-size",
author = "Samat Faieza and {Nor Farhah}, Razak",
year = "2018",
month = "6",
day = "28",
doi = "10.1063/1.5041608",
language = "English",
volume = "1974",
editor = "Hamidah Maidinsah and Sharif, {Sarifah Radiah} and Rahman, {Wan Eny Zarina Wan Abdul} and Akbarally, {Ajab Bai} and Mesliza Mohamed and Daud Mohamad and Jaffar, {Maheran Mohd}",
booktitle = "Proceeding of the 25th National Symposium on Mathematical Sciences, SKSM 2017",
publisher = "American Institute of Physics Inc.",

}

TY - GEN

T1 - Derivation of explicit 6(4) pair of hybrid methods for special second order ordinary differential equations

AU - Faieza, Samat

AU - Nor Farhah, Razak

PY - 2018/6/28

Y1 - 2018/6/28

N2 - Many physical problems can be modelled using special second order ordinary differential equations. Since someof the second order equations are either hard to be solved analytically or have no analytical solutions, therefore in the past research, there has been a continuous need for numerical methods for solving them. In this paper, the derivation of explicit 6(4) pair of hybrid methods with four stages is considered. For the higher order formula, the derivation is done by imposing the free parameter to increase the size of the interval of absolute stability. This method is implemented in variable step-size in which the lower order formula is used to approximate the local error. Numerical comparisons that have been carried out show that the new method outperforms the existing RungeKutta Nystrom 5(4) pair methodfor solving someoscillatory problems.

AB - Many physical problems can be modelled using special second order ordinary differential equations. Since someof the second order equations are either hard to be solved analytically or have no analytical solutions, therefore in the past research, there has been a continuous need for numerical methods for solving them. In this paper, the derivation of explicit 6(4) pair of hybrid methods with four stages is considered. For the higher order formula, the derivation is done by imposing the free parameter to increase the size of the interval of absolute stability. This method is implemented in variable step-size in which the lower order formula is used to approximate the local error. Numerical comparisons that have been carried out show that the new method outperforms the existing RungeKutta Nystrom 5(4) pair methodfor solving someoscillatory problems.

KW - Sixth order hybrid method

KW - Stability

KW - Variable step-size

UR - http://www.scopus.com/inward/record.url?scp=85049803489&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85049803489&partnerID=8YFLogxK

U2 - 10.1063/1.5041608

DO - 10.1063/1.5041608

M3 - Conference contribution

VL - 1974

BT - Proceeding of the 25th National Symposium on Mathematical Sciences, SKSM 2017

A2 - Maidinsah, Hamidah

A2 - Sharif, Sarifah Radiah

A2 - Rahman, Wan Eny Zarina Wan Abdul

A2 - Akbarally, Ajab Bai

A2 - Mohamed, Mesliza

A2 - Mohamad, Daud

A2 - Jaffar, Maheran Mohd

PB - American Institute of Physics Inc.

ER -