Numerical solution and stability of multistep method for solving delay differential equations.

This paper considers the numerical solution of delay differential equations. The predictor–corrector scheme based on generalized multistep methods are implemented in variable order variable stepsize techniques. The formulae are represented in divided difference form where the integration coefficient...

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Main Authors: Suleiman, Mohamed B., Ishak, Fuziyah
Format: Article
Language:English
Published: JJIAM Publishing Committee and Springer 2010
Online Access:http://psasir.upm.edu.my/id/eprint/15861/
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author Suleiman, Mohamed B.
Ishak, Fuziyah
author_facet Suleiman, Mohamed B.
Ishak, Fuziyah
author_sort Suleiman, Mohamed B.
building UPM Institutional Repository
collection Online Access
description This paper considers the numerical solution of delay differential equations. The predictor–corrector scheme based on generalized multistep methods are implemented in variable order variable stepsize techniques. The formulae are represented in divided difference form where the integration coefficients are computed by a simple recurrence relation. This representation produces simpler calculation as compared with the modified divided difference form, but no sacrifice is made in efficiency and accuracy of the method. Numerical results prove that the method is reliable, efficient and accurate. The P- and Q-stability regions for a fixed stepsize of the predictor–corrector scheme are illustrated for various orders.
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spelling upm-158612013-07-25T07:22:14Z http://psasir.upm.edu.my/id/eprint/15861/ Numerical solution and stability of multistep method for solving delay differential equations. Suleiman, Mohamed B. Ishak, Fuziyah This paper considers the numerical solution of delay differential equations. The predictor–corrector scheme based on generalized multistep methods are implemented in variable order variable stepsize techniques. The formulae are represented in divided difference form where the integration coefficients are computed by a simple recurrence relation. This representation produces simpler calculation as compared with the modified divided difference form, but no sacrifice is made in efficiency and accuracy of the method. Numerical results prove that the method is reliable, efficient and accurate. The P- and Q-stability regions for a fixed stepsize of the predictor–corrector scheme are illustrated for various orders. JJIAM Publishing Committee and Springer 2010-12 Article PeerReviewed Suleiman, Mohamed B. and Ishak, Fuziyah (2010) Numerical solution and stability of multistep method for solving delay differential equations. Japan Journal of Industrial and Applied Mathematics, 27 (3). pp. 395-410. ISSN 1868-937X 10.1007/s13160-010-0017-6 English
spellingShingle Suleiman, Mohamed B.
Ishak, Fuziyah
Numerical solution and stability of multistep method for solving delay differential equations.
title Numerical solution and stability of multistep method for solving delay differential equations.
title_full Numerical solution and stability of multistep method for solving delay differential equations.
title_fullStr Numerical solution and stability of multistep method for solving delay differential equations.
title_full_unstemmed Numerical solution and stability of multistep method for solving delay differential equations.
title_short Numerical solution and stability of multistep method for solving delay differential equations.
title_sort numerical solution and stability of multistep method for solving delay differential equations.
url http://psasir.upm.edu.my/id/eprint/15861/
http://psasir.upm.edu.my/id/eprint/15861/