Cover Image

Solving delay differential equations of small and vanishing lag using multistep block method

This paper considers the numerical solution of delay differential equations for solving the problem of small and vanishing lag using multistep block method. This problem arises when the size of a delay value is smaller than the step size, x - τ < h, and the delay time may even vanish when τ → 0 i...

Full description

Saved in:
Bibliographic Details
Main Authors: Abdul Aziz, Nurul Huda, Abdul Majid, Zanariah, Ismail, Fudziah
Format: Article
Language:English
Published: Hindawi Publishing Corporation 2014
Online Access:http://psasir.upm.edu.my/id/eprint/51855/1/51855.pdf
http://psasir.upm.edu.my/id/eprint/51855/
https://www.hindawi.com/journals/jam/2014/348912/abs/
Tags: Add Tag
No Tags, Be the first to tag this record!
id my.upm.eprints.51855
record_format eprints
spelling my.upm.eprints.518552017-05-02T08:05:13Z http://psasir.upm.edu.my/id/eprint/51855/ Solving delay differential equations of small and vanishing lag using multistep block method Abdul Aziz, Nurul Huda Abdul Majid, Zanariah Ismail, Fudziah This paper considers the numerical solution of delay differential equations for solving the problem of small and vanishing lag using multistep block method. This problem arises when the size of a delay value is smaller than the step size, x - τ < h, and the delay time may even vanish when τ → 0 in a current step. The proposed approach that is based on interpolation of Newton divided difference has been implemented by adapting this problem to the multistep block method. In order to achieve the required accuracy, this approach considered the appropriate degree of interpolation polynomial in approximating the solution of delay term. The developed code for solving small and vanishing lag is done using C program and we called it as DDEB5. The P-stability and Q-stability of this method are also studied. Numerical results are presented and compared to the existing method in order to illustrate the efficiency of the proposed method. Hindawi Publishing Corporation 2014 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/51855/1/51855.pdf Abdul Aziz, Nurul Huda and Abdul Majid, Zanariah and Ismail, Fudziah (2014) Solving delay differential equations of small and vanishing lag using multistep block method. Journal of Applied Mathematics, 2014. art. no. 348912. pp. 1-10. ISSN 1110-757X; ESSN: 1687-0042 https://www.hindawi.com/journals/jam/2014/348912/abs/ 10.1155/2014/348912
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 This paper considers the numerical solution of delay differential equations for solving the problem of small and vanishing lag using multistep block method. This problem arises when the size of a delay value is smaller than the step size, x - τ < h, and the delay time may even vanish when τ → 0 in a current step. The proposed approach that is based on interpolation of Newton divided difference has been implemented by adapting this problem to the multistep block method. In order to achieve the required accuracy, this approach considered the appropriate degree of interpolation polynomial in approximating the solution of delay term. The developed code for solving small and vanishing lag is done using C program and we called it as DDEB5. The P-stability and Q-stability of this method are also studied. Numerical results are presented and compared to the existing method in order to illustrate the efficiency of the proposed method.
format Article
author Abdul Aziz, Nurul Huda
Abdul Majid, Zanariah
Ismail, Fudziah
spellingShingle Abdul Aziz, Nurul Huda
Abdul Majid, Zanariah
Ismail, Fudziah
Solving delay differential equations of small and vanishing lag using multistep block method
author_facet Abdul Aziz, Nurul Huda
Abdul Majid, Zanariah
Ismail, Fudziah
author_sort Abdul Aziz, Nurul Huda
title Solving delay differential equations of small and vanishing lag using multistep block method
title_short Solving delay differential equations of small and vanishing lag using multistep block method
title_full Solving delay differential equations of small and vanishing lag using multistep block method
title_fullStr Solving delay differential equations of small and vanishing lag using multistep block method
title_full_unstemmed Solving delay differential equations of small and vanishing lag using multistep block method
title_sort solving delay differential equations of small and vanishing lag using multistep block method
publisher Hindawi Publishing Corporation
publishDate 2014
url http://psasir.upm.edu.my/id/eprint/51855/1/51855.pdf
http://psasir.upm.edu.my/id/eprint/51855/
https://www.hindawi.com/journals/jam/2014/348912/abs/
_version_ 1643835075793518592
score 13.211869

Similar Items