Application of the shooting method in 2-point block BDF for nonlinear boundary value problems
In this research, the boundary value problems (BVPs) are solved by applying a variable step two-point block backward differentiation formula (2BDF) in a shooting technique. An iterative procedure known as Newton-Raphson and the linear combination of the initial guesses are applied in this shooting a...
| Main Authors: | , , , , , , |
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| Format: | Article |
| Language: | English |
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International Association of Engineers
2025
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| Online Access: | https://umpir.ump.edu.my/id/eprint/45782/ |
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| author | Soomro, Hira Nooraini, Zainuddin Nor Ain Azeany, Mohd Nasir Hanita, Daud Rahimah, Jusoh Siti Ainor, Mohd Yatim Iskandar Shah, Mohd Zawawi |
| author_facet | Soomro, Hira Nooraini, Zainuddin Nor Ain Azeany, Mohd Nasir Hanita, Daud Rahimah, Jusoh Siti Ainor, Mohd Yatim Iskandar Shah, Mohd Zawawi |
| author_sort | Soomro, Hira |
| building | UMP Institutional Repository |
| collection | Online Access |
| description | In this research, the boundary value problems (BVPs) are solved by applying a variable step two-point block backward differentiation formula (2BDF) in a shooting technique. An iterative procedure known as Newton-Raphson and the linear combination of the initial guesses are applied in this shooting approach to find appropriate initial conditions for a related initial value problem (IVP) of BVP. Initially, the nonlinear BVP is reduced to the form of first-order ordinary differential equation (ODE). Subsequently, the missing IVP is approximated using the shooting technique and then solved by the 2BDF. Comparisons to exact solutions demonstrate the outcome of the proposed method for solving nonlinear BVP. The results show that the application of shooting technique is appropriate for the 2BDF to solve nonlinear BVP. |
| first_indexed | 2025-11-15T04:01:50Z |
| format | Article |
| id | ump-45782 |
| institution | Universiti Malaysia Pahang |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T04:01:50Z |
| publishDate | 2025 |
| publisher | International Association of Engineers |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | ump-457822025-10-01T08:30:06Z https://umpir.ump.edu.my/id/eprint/45782/ Application of the shooting method in 2-point block BDF for nonlinear boundary value problems Soomro, Hira Nooraini, Zainuddin Nor Ain Azeany, Mohd Nasir Hanita, Daud Rahimah, Jusoh Siti Ainor, Mohd Yatim Iskandar Shah, Mohd Zawawi QA Mathematics In this research, the boundary value problems (BVPs) are solved by applying a variable step two-point block backward differentiation formula (2BDF) in a shooting technique. An iterative procedure known as Newton-Raphson and the linear combination of the initial guesses are applied in this shooting approach to find appropriate initial conditions for a related initial value problem (IVP) of BVP. Initially, the nonlinear BVP is reduced to the form of first-order ordinary differential equation (ODE). Subsequently, the missing IVP is approximated using the shooting technique and then solved by the 2BDF. Comparisons to exact solutions demonstrate the outcome of the proposed method for solving nonlinear BVP. The results show that the application of shooting technique is appropriate for the 2BDF to solve nonlinear BVP. International Association of Engineers 2025-05-01 Article PeerReviewed pdf en https://umpir.ump.edu.my/id/eprint/45782/1/EL_33_5_21.pdf Soomro, Hira and Nooraini, Zainuddin and Nor Ain Azeany, Mohd Nasir and Hanita, Daud and Rahimah, Jusoh and Siti Ainor, Mohd Yatim and Iskandar Shah, Mohd Zawawi (2025) Application of the shooting method in 2-point block BDF for nonlinear boundary value problems. Engineering Letters, 33 (5). pp. 1405-1410. ISSN 1816-093X (Print); 1816-0948 (Online). (Published) https://www.engineeringletters.com/issues_v33/issue_5/EL_33_5_21.pdf https://www.engineeringletters.com/issues_v33/issue_5/EL_33_5_21.pdf https://www.engineeringletters.com/issues_v33/issue_5/EL_33_5_21.pdf |
| spellingShingle | QA Mathematics Soomro, Hira Nooraini, Zainuddin Nor Ain Azeany, Mohd Nasir Hanita, Daud Rahimah, Jusoh Siti Ainor, Mohd Yatim Iskandar Shah, Mohd Zawawi Application of the shooting method in 2-point block BDF for nonlinear boundary value problems |
| title | Application of the shooting method in 2-point block BDF for nonlinear boundary value problems |
| title_full | Application of the shooting method in 2-point block BDF for nonlinear boundary value problems |
| title_fullStr | Application of the shooting method in 2-point block BDF for nonlinear boundary value problems |
| title_full_unstemmed | Application of the shooting method in 2-point block BDF for nonlinear boundary value problems |
| title_short | Application of the shooting method in 2-point block BDF for nonlinear boundary value problems |
| title_sort | application of the shooting method in 2-point block bdf for nonlinear boundary value problems |
| topic | QA Mathematics |
| url | https://umpir.ump.edu.my/id/eprint/45782/ https://umpir.ump.edu.my/id/eprint/45782/ https://umpir.ump.edu.my/id/eprint/45782/ |