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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Hindawi
2018
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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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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 |
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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. |
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Ghawadri, Nizam Ghannam Fayez Senu, Norazak Ismail, Fudziah Ibrahim, Zarina Bibi |
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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/ |
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1685580233301819392 |
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13.18916 |