An accurate block hybrid collocation method for third order ordinary differential equations
The block hybrid collocation method with two off-step points is proposed for the direct solution of general third order ordinary differential equations. Both the main and additional methods are derived via interpolation and collocation of the basic polynomial. These methods are applied in block form...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Hindawi Publishing Corporation
2014
|
| Online Access: | http://psasir.upm.edu.my/id/eprint/36381/1/An%20accurate%20block%20hybrid%20collocation%20method%20for%20third%20order%20ordinary%20differential%20equations.pdf |
| _version_ | 1796972900475994112 |
|---|---|
| author | Yap, Lee Ken Ismail, Fudziah Senu, Norazak |
| author_facet | Yap, Lee Ken Ismail, Fudziah Senu, Norazak |
| author_sort | Yap, Lee Ken |
| collection | UPM |
| description | The block hybrid collocation method with two off-step points is proposed for the direct solution of general third order ordinary differential equations. Both the main and additional methods are derived via interpolation and collocation of the basic polynomial. These methods are applied in block form to provide the approximation at five points concurrently. The stability properties of the block method are investigated. Some numerical examples are tested to illustrate the efficiency of the method. The block hybrid collocation method is also implemented to solve the nonlinear Genesio equation and the problem in thin film flow. |
| first_indexed | 2024-03-06T08:35:09Z |
| format | Article |
| id | upm.eprints-36381 |
| institution | Universiti Putra Malaysia |
| language | English |
| last_indexed | 2024-03-06T08:35:09Z |
| publishDate | 2014 |
| publisher | Hindawi Publishing Corporation |
| record_format | dspace |
| spelling | upm.eprints-363812015-10-23T03:04:56Z http://psasir.upm.edu.my/id/eprint/36381/ An accurate block hybrid collocation method for third order ordinary differential equations Yap, Lee Ken Ismail, Fudziah Senu, Norazak The block hybrid collocation method with two off-step points is proposed for the direct solution of general third order ordinary differential equations. Both the main and additional methods are derived via interpolation and collocation of the basic polynomial. These methods are applied in block form to provide the approximation at five points concurrently. The stability properties of the block method are investigated. Some numerical examples are tested to illustrate the efficiency of the method. The block hybrid collocation method is also implemented to solve the nonlinear Genesio equation and the problem in thin film flow. Hindawi Publishing Corporation 2014 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/36381/1/An%20accurate%20block%20hybrid%20collocation%20method%20for%20third%20order%20ordinary%20differential%20equations.pdf Yap, Lee Ken and Ismail, Fudziah and Senu, Norazak (2014) An accurate block hybrid collocation method for third order ordinary differential equations. Journal of Applied Mathematics, 2014. art. no. 549597. pp. 1-9. ISSN 1110-757X; ESSN:1687-0042 http://www.hindawi.com/journals/jam/2014/549597/abs/ 10.1155/2014/549597 |
| spellingShingle | Yap, Lee Ken Ismail, Fudziah Senu, Norazak An accurate block hybrid collocation method for third order ordinary differential equations |
| title | An accurate block hybrid collocation method for third order ordinary differential equations |
| title_full | An accurate block hybrid collocation method for third order ordinary differential equations |
| title_fullStr | An accurate block hybrid collocation method for third order ordinary differential equations |
| title_full_unstemmed | An accurate block hybrid collocation method for third order ordinary differential equations |
| title_short | An accurate block hybrid collocation method for third order ordinary differential equations |
| title_sort | accurate block hybrid collocation method for third order ordinary differential equations |
| url | http://psasir.upm.edu.my/id/eprint/36381/1/An%20accurate%20block%20hybrid%20collocation%20method%20for%20third%20order%20ordinary%20differential%20equations.pdf |
| work_keys_str_mv | AT yapleeken anaccurateblockhybridcollocationmethodforthirdorderordinarydifferentialequations AT ismailfudziah anaccurateblockhybridcollocationmethodforthirdorderordinarydifferentialequations AT senunorazak anaccurateblockhybridcollocationmethodforthirdorderordinarydifferentialequations AT yapleeken accurateblockhybridcollocationmethodforthirdorderordinarydifferentialequations AT ismailfudziah accurateblockhybridcollocationmethodforthirdorderordinarydifferentialequations AT senunorazak accurateblockhybridcollocationmethodforthirdorderordinarydifferentialequations |