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 |
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Universiti Kebangsaan Malaysia
2009
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| Online Access: | http://journalarticle.ukm.my/13/ http://journalarticle.ukm.my/13/1/ |
| _version_ | 1848809120401981440 |
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| author | Mahanum Diana Jafri, Mohamed Suleiman, Zanariah Abdul Majid, Zarina Bibi Ibrahim, |
| author_facet | Mahanum Diana Jafri, Mohamed Suleiman, Zanariah Abdul Majid, Zarina Bibi Ibrahim, |
| author_sort | Mahanum Diana Jafri, |
| building | UKM 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 | 2025-11-14T23:09:34Z |
| format | Article |
| id | ukm-13 |
| institution | Universiti Kebangasaan Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-14T23:09:34Z |
| publishDate | 2009 |
| publisher | Universiti Kebangsaan Malaysia |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | ukm-132016-12-14T06:26:11Z http://journalarticle.ukm.my/13/ Solving directly two point boundary value problems using direct multistep method Mahanum Diana Jafri, Mohamed Suleiman, Zanariah Abdul Majid, Zarina Bibi Ibrahim, 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. Universiti Kebangsaan Malaysia 2009-10 Article PeerReviewed application/pdf en http://journalarticle.ukm.my/13/1/ Mahanum Diana Jafri, and Mohamed Suleiman, and Zanariah Abdul Majid, and Zarina Bibi Ibrahim, (2009) Solving directly two point boundary value problems using direct multistep method. Sains Malaysiana, 38 (5). pp. 723-728. ISSN 0126-6039 http://www.ukm.my/~jsm/kandungan.html |
| spellingShingle | Mahanum Diana Jafri, Mohamed Suleiman, Zanariah Abdul Majid, Zarina Bibi Ibrahim, 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 |
| url | http://journalarticle.ukm.my/13/ http://journalarticle.ukm.my/13/ http://journalarticle.ukm.my/13/1/ |