Numerical computation of third order delay differential equations by using direct multistep method
This paper introduces a direct multistep method to solve third order delay differential equations (DDEs) based on the boundary conditions given. The multistep method is presented in direct integration approach to reduce the total function calls involved and the method is derived implicitly so that...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Institute for Mathematical Research, Universiti Putra Malaysia
2021
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| Online Access: | http://psasir.upm.edu.my/id/eprint/94390/ http://psasir.upm.edu.my/id/eprint/94390/1/Numerical%20Computation%20of%20Third%20Order%20Delay%20Differential%20Equations.pdf |
| _version_ | 1848861984146063360 |
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| author | Jaaffar, N. T. Majid, Z. A. Senu, N. |
| author_facet | Jaaffar, N. T. Majid, Z. A. Senu, N. |
| author_sort | Jaaffar, N. T. |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | This paper introduces a direct multistep method to solve third order delay differential equations
(DDEs) based on the boundary conditions given. The multistep method is presented in direct
integration approach to reduce the total function calls involved and the method is derived implicitly so that the accuracy is attained. The method is also in block for every iteration to reduce
total steps taken. The DDEs involve the endpoints of boundary conditions, hence, the shooting
technique is to choose for the best value of additional initial value. The constant and pantograph delay types are the DDEs problems considered in this study. Lagrange interpolation is
used to interpolate the delay involved in pantograph problems. The observation of the multistep method in terms of order, consistency, and convergence is also presented in this paper.
The numerical results obtained are compared with the previous multistep method to verify the
capability of the proposed method to solve third order DDEs directly. |
| first_indexed | 2025-11-15T13:09:48Z |
| format | Article |
| id | upm-94390 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T13:09:48Z |
| publishDate | 2021 |
| publisher | Institute for Mathematical Research, Universiti Putra Malaysia |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-943902023-04-05T02:00:40Z http://psasir.upm.edu.my/id/eprint/94390/ Numerical computation of third order delay differential equations by using direct multistep method Jaaffar, N. T. Majid, Z. A. Senu, N. This paper introduces a direct multistep method to solve third order delay differential equations (DDEs) based on the boundary conditions given. The multistep method is presented in direct integration approach to reduce the total function calls involved and the method is derived implicitly so that the accuracy is attained. The method is also in block for every iteration to reduce total steps taken. The DDEs involve the endpoints of boundary conditions, hence, the shooting technique is to choose for the best value of additional initial value. The constant and pantograph delay types are the DDEs problems considered in this study. Lagrange interpolation is used to interpolate the delay involved in pantograph problems. The observation of the multistep method in terms of order, consistency, and convergence is also presented in this paper. The numerical results obtained are compared with the previous multistep method to verify the capability of the proposed method to solve third order DDEs directly. Institute for Mathematical Research, Universiti Putra Malaysia 2021-06-22 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/94390/1/Numerical%20Computation%20of%20Third%20Order%20Delay%20Differential%20Equations.pdf Jaaffar, N. T. and Majid, Z. A. and Senu, N. (2021) Numerical computation of third order delay differential equations by using direct multistep method. Malaysian Journal of Mathematical Sciences, 15 (3). 369 - 385. ISSN 1823-8343; ESSN: 2289-750X https://mjms.upm.edu.my/lihatmakalah.php?kod=2021/September/15/3/369-385 |
| spellingShingle | Jaaffar, N. T. Majid, Z. A. Senu, N. Numerical computation of third order delay differential equations by using direct multistep method |
| title | Numerical computation of third order delay differential equations by using direct multistep method |
| title_full | Numerical computation of third order delay differential equations by using direct multistep method |
| title_fullStr | Numerical computation of third order delay differential equations by using direct multistep method |
| title_full_unstemmed | Numerical computation of third order delay differential equations by using direct multistep method |
| title_short | Numerical computation of third order delay differential equations by using direct multistep method |
| title_sort | numerical computation of third order delay differential equations by using direct multistep method |
| url | http://psasir.upm.edu.my/id/eprint/94390/ http://psasir.upm.edu.my/id/eprint/94390/ http://psasir.upm.edu.my/id/eprint/94390/1/Numerical%20Computation%20of%20Third%20Order%20Delay%20Differential%20Equations.pdf |