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Exponentially fitted and trigonometrically fitted explicit modified Runge-Kutta type methods for solving y’’’ (x)=f (x,y,y’)

Exponentially fitted and trigonometrically fitted explicit modified Runge-Kutta type (MRKT) methods for solving y’’’ (x)=f (x,y,y’) are derived in this paper. These methods are constructed which exactly integrate initial value problems whose solutions are linear combinations of the set functions ewx...

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Main Authors: Ghawadri, Nizam Ghannam Fayez, Senu, Norazak, Ismail, Fudziah, Ibrahim, Zarina Bibi
Format: Article
Language:English
Published: Hindawi 2018
Online Access:http://psasir.upm.edu.my/id/eprint/72681/1/Exponentially%20fitted%20and%20trigonometrically%20fitted%20explicit.pdf
http://psasir.upm.edu.my/id/eprint/72681/
https://www.hindawi.com/journals/jam/2018/4029371/
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spelling my.upm.eprints.726812020-11-30T08:58:42Z http://psasir.upm.edu.my/id/eprint/72681/ Exponentially fitted and trigonometrically fitted explicit modified Runge-Kutta type methods for solving y’’’ (x)=f (x,y,y’) Ghawadri, Nizam Ghannam Fayez Senu, Norazak Ismail, Fudziah Ibrahim, Zarina Bibi Exponentially fitted and trigonometrically fitted explicit modified Runge-Kutta type (MRKT) methods for solving y’’’ (x)=f (x,y,y’) are derived in this paper. These methods are constructed which exactly integrate initial value problems whose solutions are linear combinations of the set functions ewx and e-wx for exponentially fitted sin(wx) and cos (wx) for trigonometrically fitted with w ᗴ r being the principal frequency of the problem and the frequency will be used to raise the accuracy of the methods. The new four-stage fifth-order exponentially fitted and trigonometrically fitted explicit MRKT methods are called EFMRKT5 and TFMRKT5, respectively, for solving initial value problems whose solutions involve exponential or trigonometric functions. The numerical results indicate that the new exponentially fitted and trigonometrically fitted explicit modified Runge-Kutta type methods are more efficient than existing methods in the literature. Hindawi 2018 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/72681/1/Exponentially%20fitted%20and%20trigonometrically%20fitted%20explicit.pdf Ghawadri, Nizam Ghannam Fayez and Senu, Norazak and Ismail, Fudziah and Ibrahim, Zarina Bibi (2018) Exponentially fitted and trigonometrically fitted explicit modified Runge-Kutta type methods for solving y’’’ (x)=f (x,y,y’). Journal of Applied Mathematics, 2018. art. no. 4029371. pp. 1-19. ISSN 1110-757X; ESSN: 1687-0042 https://www.hindawi.com/journals/jam/2018/4029371/ 10.1155/2018/4029371
institution Universiti Putra Malaysia
building UPM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Putra Malaysia
content_source UPM Institutional Repository
url_provider http://psasir.upm.edu.my/
language English
description Exponentially fitted and trigonometrically fitted explicit modified Runge-Kutta type (MRKT) methods for solving y’’’ (x)=f (x,y,y’) are derived in this paper. These methods are constructed which exactly integrate initial value problems whose solutions are linear combinations of the set functions ewx and e-wx for exponentially fitted sin(wx) and cos (wx) for trigonometrically fitted with w ᗴ r being the principal frequency of the problem and the frequency will be used to raise the accuracy of the methods. The new four-stage fifth-order exponentially fitted and trigonometrically fitted explicit MRKT methods are called EFMRKT5 and TFMRKT5, respectively, for solving initial value problems whose solutions involve exponential or trigonometric functions. The numerical results indicate that the new exponentially fitted and trigonometrically fitted explicit modified Runge-Kutta type methods are more efficient than existing methods in the literature.
format Article
author Ghawadri, Nizam Ghannam Fayez
Senu, Norazak
Ismail, Fudziah
Ibrahim, Zarina Bibi
spellingShingle Ghawadri, Nizam Ghannam Fayez
Senu, Norazak
Ismail, Fudziah
Ibrahim, Zarina Bibi
Exponentially fitted and trigonometrically fitted explicit modified Runge-Kutta type methods for solving y’’’ (x)=f (x,y,y’)
author_facet Ghawadri, Nizam Ghannam Fayez
Senu, Norazak
Ismail, Fudziah
Ibrahim, Zarina Bibi
author_sort Ghawadri, Nizam Ghannam Fayez
title Exponentially fitted and trigonometrically fitted explicit modified Runge-Kutta type methods for solving y’’’ (x)=f (x,y,y’)
title_short Exponentially fitted and trigonometrically fitted explicit modified Runge-Kutta type methods for solving y’’’ (x)=f (x,y,y’)
title_full Exponentially fitted and trigonometrically fitted explicit modified Runge-Kutta type methods for solving y’’’ (x)=f (x,y,y’)
title_fullStr Exponentially fitted and trigonometrically fitted explicit modified Runge-Kutta type methods for solving y’’’ (x)=f (x,y,y’)
title_full_unstemmed Exponentially fitted and trigonometrically fitted explicit modified Runge-Kutta type methods for solving y’’’ (x)=f (x,y,y’)
title_sort exponentially fitted and trigonometrically fitted explicit modified runge-kutta type methods for solving y’’’ (x)=f (x,y,y’)
publisher Hindawi
publishDate 2018
url http://psasir.upm.edu.my/id/eprint/72681/1/Exponentially%20fitted%20and%20trigonometrically%20fitted%20explicit.pdf
http://psasir.upm.edu.my/id/eprint/72681/
https://www.hindawi.com/journals/jam/2018/4029371/
_version_ 1685580233301819392
score 13.211869

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