Fourth order four-stage diagonally implicit Runge-Kutta method for linear ordinary differential equations
A new fourth order four-stage diagonally Implicit Runge-Kutta (DIRK) method which is specially designed for the integration of Linear Ordinary Differential Equations (LODEs) is constructed. In the derivation, Butcher's error equations are used but one of the error equations can be eliminated du...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Universiti Putra Malaysia Press
2010
|
| Online Access: | http://psasir.upm.edu.my/id/eprint/14811/ http://psasir.upm.edu.my/id/eprint/14811/1/14811.pdf |
| _version_ | 1848842500109762560 |
|---|---|
| author | Che Jawias, Nur Izzati Ismail, Fudziah Suleiman, Mohamed Jaafar, Azmi |
| author_facet | Che Jawias, Nur Izzati Ismail, Fudziah Suleiman, Mohamed Jaafar, Azmi |
| author_sort | Che Jawias, Nur Izzati |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | A new fourth order four-stage diagonally Implicit Runge-Kutta (DIRK) method which is specially designed for the integration of Linear Ordinary Differential Equations (LODEs) is constructed. In the derivation, Butcher's error equations are used but one of the error equations can be eliminated due to the property of the LODE itself. The stability aspect of the method is investigated and it is found to have a bigger region of stability compared to explicit Runge-Kutta (ERK) method of the same type (designed for the integration of LODE). A set of test problems are used to validate the method and numerical results show that the method produced smaller global error compared to ERK method. |
| first_indexed | 2025-11-15T08:00:07Z |
| format | Article |
| id | upm-14811 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T08:00:07Z |
| publishDate | 2010 |
| publisher | Universiti Putra Malaysia Press |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-148112015-05-27T06:37:52Z http://psasir.upm.edu.my/id/eprint/14811/ Fourth order four-stage diagonally implicit Runge-Kutta method for linear ordinary differential equations Che Jawias, Nur Izzati Ismail, Fudziah Suleiman, Mohamed Jaafar, Azmi A new fourth order four-stage diagonally Implicit Runge-Kutta (DIRK) method which is specially designed for the integration of Linear Ordinary Differential Equations (LODEs) is constructed. In the derivation, Butcher's error equations are used but one of the error equations can be eliminated due to the property of the LODE itself. The stability aspect of the method is investigated and it is found to have a bigger region of stability compared to explicit Runge-Kutta (ERK) method of the same type (designed for the integration of LODE). A set of test problems are used to validate the method and numerical results show that the method produced smaller global error compared to ERK method. Universiti Putra Malaysia Press 2010 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/14811/1/14811.pdf Che Jawias, Nur Izzati and Ismail, Fudziah and Suleiman, Mohamed and Jaafar, Azmi (2010) Fourth order four-stage diagonally implicit Runge-Kutta method for linear ordinary differential equations. Malaysian Journal of Mathematical Sciences, 4 (1). pp. 95-105. ISSN 1823-8343 http://einspem.upm.edu.my/journal/volume4.1.php |
| spellingShingle | Che Jawias, Nur Izzati Ismail, Fudziah Suleiman, Mohamed Jaafar, Azmi Fourth order four-stage diagonally implicit Runge-Kutta method for linear ordinary differential equations |
| title | Fourth order four-stage diagonally implicit Runge-Kutta method for linear ordinary differential equations |
| title_full | Fourth order four-stage diagonally implicit Runge-Kutta method for linear ordinary differential equations |
| title_fullStr | Fourth order four-stage diagonally implicit Runge-Kutta method for linear ordinary differential equations |
| title_full_unstemmed | Fourth order four-stage diagonally implicit Runge-Kutta method for linear ordinary differential equations |
| title_short | Fourth order four-stage diagonally implicit Runge-Kutta method for linear ordinary differential equations |
| title_sort | fourth order four-stage diagonally implicit runge-kutta method for linear ordinary differential equations |
| url | http://psasir.upm.edu.my/id/eprint/14811/ http://psasir.upm.edu.my/id/eprint/14811/ http://psasir.upm.edu.my/id/eprint/14811/1/14811.pdf |