Two point block method in variable stepsize technique for solving delay differential equations
Delay differential equations play an important role in modeling many real life phenomena. The application areas of delay differential equations include the fields of engineering, biology and economy. In this paper, we describe the development and the stability analysis of a two-point implicit block...
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| Format: | Article |
| Language: | English |
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David Publishing Company
2010
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| Online Access: | http://psasir.upm.edu.my/id/eprint/17500/ http://psasir.upm.edu.my/id/eprint/17500/1/Two-Point%20Block%20Method%20in%20Variable%20Stepsize%20Technique.pdf |
| _version_ | 1848843258619232256 |
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| author | Ishak, Fuziyah Abdul Majid, Zanariah Suleiman, Mohamed |
| author_facet | Ishak, Fuziyah Abdul Majid, Zanariah Suleiman, Mohamed |
| author_sort | Ishak, Fuziyah |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | Delay differential equations play an important role in modeling many real life phenomena. The application areas of delay differential equations include the fields of engineering, biology and economy. In this paper, we describe the development and the stability analysis of a two-point implicit block method for solving delay differential equations. The method produces two new values at a single step of integration. The implicit formulae are derived by using a predictor of order four and a corrector of order five. The method is implemented by using the variable stepsize technique and the predictor-corrector scheme is iterated until convergence. In variable stepsize approach, the integration coefficients need to be recalculated whenever a step size changes. These tedious calculations are avoided by deriving the formulae beforehand and storing the coefficients at the start of the code. In preserving the order of the method, the number of interpolation points for approximating delay solution is one higher than the order of the method at grid point. The numerical results suggest that the two-point implicit block method provides an efficient, reliable and accurate way of solving a
wide range of delay differential equations. We also consider the stability analysis of the two-point block method by numerically examining the stability polynomials of the method. P-and Q-stability regions for the variable stepsize formulae are illustrated. |
| first_indexed | 2025-11-15T08:12:10Z |
| format | Article |
| id | upm-17500 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T08:12:10Z |
| publishDate | 2010 |
| publisher | David Publishing Company |
| recordtype | eprints |
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| spelling | upm-175002015-09-01T01:14:57Z http://psasir.upm.edu.my/id/eprint/17500/ Two point block method in variable stepsize technique for solving delay differential equations Ishak, Fuziyah Abdul Majid, Zanariah Suleiman, Mohamed Delay differential equations play an important role in modeling many real life phenomena. The application areas of delay differential equations include the fields of engineering, biology and economy. In this paper, we describe the development and the stability analysis of a two-point implicit block method for solving delay differential equations. The method produces two new values at a single step of integration. The implicit formulae are derived by using a predictor of order four and a corrector of order five. The method is implemented by using the variable stepsize technique and the predictor-corrector scheme is iterated until convergence. In variable stepsize approach, the integration coefficients need to be recalculated whenever a step size changes. These tedious calculations are avoided by deriving the formulae beforehand and storing the coefficients at the start of the code. In preserving the order of the method, the number of interpolation points for approximating delay solution is one higher than the order of the method at grid point. The numerical results suggest that the two-point implicit block method provides an efficient, reliable and accurate way of solving a wide range of delay differential equations. We also consider the stability analysis of the two-point block method by numerically examining the stability polynomials of the method. P-and Q-stability regions for the variable stepsize formulae are illustrated. David Publishing Company 2010-12 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/17500/1/Two-Point%20Block%20Method%20in%20Variable%20Stepsize%20Technique.pdf Ishak, Fuziyah and Abdul Majid, Zanariah and Suleiman, Mohamed (2010) Two point block method in variable stepsize technique for solving delay differential equations. Journal of Materials Science and Engineering, 4 (12). pp. 86-90. ISSN 1934-8959 http://www.davidpublishing.com/show.html?17199 |
| spellingShingle | Ishak, Fuziyah Abdul Majid, Zanariah Suleiman, Mohamed Two point block method in variable stepsize technique for solving delay differential equations |
| title | Two point block method in variable stepsize technique for solving delay differential equations |
| title_full | Two point block method in variable stepsize technique for solving delay differential equations |
| title_fullStr | Two point block method in variable stepsize technique for solving delay differential equations |
| title_full_unstemmed | Two point block method in variable stepsize technique for solving delay differential equations |
| title_short | Two point block method in variable stepsize technique for solving delay differential equations |
| title_sort | two point block method in variable stepsize technique for solving delay differential equations |
| url | http://psasir.upm.edu.my/id/eprint/17500/ http://psasir.upm.edu.my/id/eprint/17500/ http://psasir.upm.edu.my/id/eprint/17500/1/Two-Point%20Block%20Method%20in%20Variable%20Stepsize%20Technique.pdf |