A fourth-order one-step block method for solving a stiff ordinary differential equation
In this paper, we propose an A-stable one-step block method of order four for solving a stiff ordinary differential equation. This method will approximate the solutions of a stiff ordinary differential equation at three points simultaneously using a constant step size. The method is similar to the o...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Pushpa Publishing House
2016
|
| Online Access: | http://psasir.upm.edu.my/id/eprint/56243/ http://psasir.upm.edu.my/id/eprint/56243/1/A%20fourth-order%20one-step%20block%20method%20for%20solving%20a%20stiff%20ordinary%20differential%20equation.pdf |
| _version_ | 1848853027904028672 |
|---|---|
| author | Mohd Zabidi, Muhammad Izzat Zakwan Abdul Majid, Zanariah Senu, Norazak |
| author_facet | Mohd Zabidi, Muhammad Izzat Zakwan Abdul Majid, Zanariah Senu, Norazak |
| author_sort | Mohd Zabidi, Muhammad Izzat Zakwan |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | In this paper, we propose an A-stable one-step block method of order four for solving a stiff ordinary differential equation. This method will approximate the solutions of a stiff ordinary differential equation at three points simultaneously using a constant step size. The method is similar to the one-step method and it is self-starting but the implementation is based on the predictor-and-corrector formulae. Several problems have been tested in this paper to prove the efficiency and accuracy of this method. Numerical results are presented to illustrate the performance of the proposed method. The results clearly show that the proposed method is able to produce comparable and better results compared to the existing methods when solving stiff differential equations. |
| first_indexed | 2025-11-15T10:47:27Z |
| format | Article |
| id | upm-56243 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T10:47:27Z |
| publishDate | 2016 |
| publisher | Pushpa Publishing House |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-562432017-07-04T03:03:08Z http://psasir.upm.edu.my/id/eprint/56243/ A fourth-order one-step block method for solving a stiff ordinary differential equation Mohd Zabidi, Muhammad Izzat Zakwan Abdul Majid, Zanariah Senu, Norazak In this paper, we propose an A-stable one-step block method of order four for solving a stiff ordinary differential equation. This method will approximate the solutions of a stiff ordinary differential equation at three points simultaneously using a constant step size. The method is similar to the one-step method and it is self-starting but the implementation is based on the predictor-and-corrector formulae. Several problems have been tested in this paper to prove the efficiency and accuracy of this method. Numerical results are presented to illustrate the performance of the proposed method. The results clearly show that the proposed method is able to produce comparable and better results compared to the existing methods when solving stiff differential equations. Pushpa Publishing House 2016 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/56243/1/A%20fourth-order%20one-step%20block%20method%20for%20solving%20a%20stiff%20ordinary%20differential%20equation.pdf Mohd Zabidi, Muhammad Izzat Zakwan and Abdul Majid, Zanariah and Senu, Norazak (2016) A fourth-order one-step block method for solving a stiff ordinary differential equation. Far East Journal of Mathematical Sciences, 99 (12). pp. 1811-1831. ISSN 0972-0871 |
| spellingShingle | Mohd Zabidi, Muhammad Izzat Zakwan Abdul Majid, Zanariah Senu, Norazak A fourth-order one-step block method for solving a stiff ordinary differential equation |
| title | A fourth-order one-step block method for solving a stiff ordinary differential equation |
| title_full | A fourth-order one-step block method for solving a stiff ordinary differential equation |
| title_fullStr | A fourth-order one-step block method for solving a stiff ordinary differential equation |
| title_full_unstemmed | A fourth-order one-step block method for solving a stiff ordinary differential equation |
| title_short | A fourth-order one-step block method for solving a stiff ordinary differential equation |
| title_sort | fourth-order one-step block method for solving a stiff ordinary differential equation |
| url | http://psasir.upm.edu.my/id/eprint/56243/ http://psasir.upm.edu.my/id/eprint/56243/1/A%20fourth-order%20one-step%20block%20method%20for%20solving%20a%20stiff%20ordinary%20differential%20equation.pdf |