Solving directly two point boundary value problems using direct multistep method.
In this paper we consider solving directly two point boundary value problems (BVPs) for second-order ordinary differential equations (ODEs). We are concerned with solving this problem using multistep method in term of backward difference formula and approximating the solutions with the shooting meth...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English English |
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Penerbit UKM
2009
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| Online Access: | http://psasir.upm.edu.my/id/eprint/16774/ http://psasir.upm.edu.my/id/eprint/16774/1/Solving%20directly%20two%20point%20boundary%20value%20problems%20using%20direct%20multistep%20method.pdf |
| _version_ | 1848843055651618816 |
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| author | Jafri, Mahanum Diana Suleiman, Mohamed Abdul Majid, Zanariah Ibrahim, Zarina Bibi |
| author_facet | Jafri, Mahanum Diana Suleiman, Mohamed Abdul Majid, Zanariah Ibrahim, Zarina Bibi |
| author_sort | Jafri, Mahanum Diana |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | In this paper we consider solving directly two point boundary value problems (BVPs) for second-order ordinary differential equations (ODEs). We are concerned with solving this problem using multistep method in term of backward difference formula and approximating the solutions with the shooting method. Most of the existence researches involved BVPs will reduce the problem to a system of first order ODEs. This approach is very well established but it obviously will enlarge the system of first order equations. However, the direct multistep method in this paper will be utilised to obtain a series solution of the initial value problems directly without reducing to first order equations. The numerical results show that the proposed method with shooting method can produce good results. |
| first_indexed | 2025-11-15T08:08:57Z |
| format | Article |
| id | upm-16774 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English English |
| last_indexed | 2025-11-15T08:08:57Z |
| publishDate | 2009 |
| publisher | Penerbit UKM |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-167742015-10-09T00:46:13Z http://psasir.upm.edu.my/id/eprint/16774/ Solving directly two point boundary value problems using direct multistep method. Jafri, Mahanum Diana Suleiman, Mohamed Abdul Majid, Zanariah Ibrahim, Zarina Bibi In this paper we consider solving directly two point boundary value problems (BVPs) for second-order ordinary differential equations (ODEs). We are concerned with solving this problem using multistep method in term of backward difference formula and approximating the solutions with the shooting method. Most of the existence researches involved BVPs will reduce the problem to a system of first order ODEs. This approach is very well established but it obviously will enlarge the system of first order equations. However, the direct multistep method in this paper will be utilised to obtain a series solution of the initial value problems directly without reducing to first order equations. The numerical results show that the proposed method with shooting method can produce good results. Penerbit UKM 2009-10 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/16774/1/Solving%20directly%20two%20point%20boundary%20value%20problems%20using%20direct%20multistep%20method.pdf Jafri, Mahanum Diana and Suleiman, Mohamed and Abdul Majid, Zanariah and Ibrahim, Zarina Bibi (2009) Solving directly two point boundary value problems using direct multistep method. Sains Malaysiana, 38 (5). pp. 723-728. ISSN 0126-6039 Boundary value problems Differential equations English |
| spellingShingle | Boundary value problems Differential equations Jafri, Mahanum Diana Suleiman, Mohamed Abdul Majid, Zanariah Ibrahim, Zarina Bibi Solving directly two point boundary value problems using direct multistep method. |
| title | Solving directly two point boundary value problems using direct multistep method. |
| title_full | Solving directly two point boundary value problems using direct multistep method. |
| title_fullStr | Solving directly two point boundary value problems using direct multistep method. |
| title_full_unstemmed | Solving directly two point boundary value problems using direct multistep method. |
| title_short | Solving directly two point boundary value problems using direct multistep method. |
| title_sort | solving directly two point boundary value problems using direct multistep method. |
| topic | Boundary value problems Differential equations |
| url | http://psasir.upm.edu.my/id/eprint/16774/ http://psasir.upm.edu.my/id/eprint/16774/1/Solving%20directly%20two%20point%20boundary%20value%20problems%20using%20direct%20multistep%20method.pdf |