Solution of higher order ODEs using backward difference method.
The current numerical technique for solving a system of higher-order ordinary differential equations (ODEs) is to reduce it to a system of first-order equations then solving it using first-order ODE methods. Here, we propose a method to solve higher-order ODEs directly. The formulae will be derived...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Hindawi Publishing Corporation
2011
|
| Online Access: | http://psasir.upm.edu.my/id/eprint/25025/ |
| _version_ | 1848845196854296576 |
|---|---|
| author | Suleiman, Mohamed Ibrahim, Zarina Bibi Rasedee, Ahmad Fadly Nurullah |
| author_facet | Suleiman, Mohamed Ibrahim, Zarina Bibi Rasedee, Ahmad Fadly Nurullah |
| author_sort | Suleiman, Mohamed |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | The current numerical technique for solving a system of higher-order ordinary differential equations (ODEs) is to reduce it to a system of first-order equations then solving it using first-order ODE methods. Here, we propose a method to solve higher-order ODEs directly. The formulae will be derived in terms of backward difference in a constant stepsize formulation. The method developed will be validated by solving some higher-order ODEs directly with constant stepsize. To simplify the evaluations of the integration coefficients, we find the relationship between various orders. The result presented confirmed our hypothesis. |
| first_indexed | 2025-11-15T08:42:59Z |
| format | Article |
| id | upm-25025 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T08:42:59Z |
| publishDate | 2011 |
| publisher | Hindawi Publishing Corporation |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-250252013-08-02T08:03:44Z http://psasir.upm.edu.my/id/eprint/25025/ Solution of higher order ODEs using backward difference method. Suleiman, Mohamed Ibrahim, Zarina Bibi Rasedee, Ahmad Fadly Nurullah The current numerical technique for solving a system of higher-order ordinary differential equations (ODEs) is to reduce it to a system of first-order equations then solving it using first-order ODE methods. Here, we propose a method to solve higher-order ODEs directly. The formulae will be derived in terms of backward difference in a constant stepsize formulation. The method developed will be validated by solving some higher-order ODEs directly with constant stepsize. To simplify the evaluations of the integration coefficients, we find the relationship between various orders. The result presented confirmed our hypothesis. Hindawi Publishing Corporation 2011 Article PeerReviewed Suleiman, Mohamed and Ibrahim, Zarina Bibi and Rasedee, Ahmad Fadly Nurullah (2011) Solution of higher order ODEs using backward difference method. Mathematical Problems in Engineering, 2011 (810324). pp. 1-18. ISSN 1024-123X http://www.hindawi.com/ 10.1155/2011/810324 English |
| spellingShingle | Suleiman, Mohamed Ibrahim, Zarina Bibi Rasedee, Ahmad Fadly Nurullah Solution of higher order ODEs using backward difference method. |
| title | Solution of higher order ODEs using backward difference method. |
| title_full | Solution of higher order ODEs using backward difference method. |
| title_fullStr | Solution of higher order ODEs using backward difference method. |
| title_full_unstemmed | Solution of higher order ODEs using backward difference method. |
| title_short | Solution of higher order ODEs using backward difference method. |
| title_sort | solution of higher order odes using backward difference method. |
| url | http://psasir.upm.edu.my/id/eprint/25025/ http://psasir.upm.edu.my/id/eprint/25025/ http://psasir.upm.edu.my/id/eprint/25025/ |