Two-point diagonally implicit multistep block method for solving Robin boundary value problems using variable step size strategy
This study focuses on the multistep integration method for approximating directly the solutions of the second order boundary value problems (BVPs) with Robin boundary conditions. The derivation of the predictor and corrector formulas uses Lagrange interpolation polynomial in the form of Adam's...
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| Format: | Article |
| Language: | English |
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Akademi Sains Malaysia
2019
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| Online Access: | http://umpir.ump.edu.my/id/eprint/32341/ http://umpir.ump.edu.my/id/eprint/32341/1/PAPER%202.pdf |
| _version_ | 1848823997842587648 |
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| author | Nadirah, Mohd Nasir Zanariah, Abdul Majid Fudziah, Ismail Norfifah, Bachok |
| author_facet | Nadirah, Mohd Nasir Zanariah, Abdul Majid Fudziah, Ismail Norfifah, Bachok |
| author_sort | Nadirah, Mohd Nasir |
| building | UMP Institutional Repository |
| collection | Online Access |
| description | This study focuses on the multistep integration method for approximating directly the solutions of the second order boundary value problems (BVPs) with Robin boundary conditions. The derivation of the predictor and corrector formulas uses Lagrange interpolation polynomial in the form of Adam's method. Two numerical solutions are computed concurrently within a block method with non-uniformly step size. The implementation of multistep block method follows the m PE(CE) procedure via shooting technique. Newton divided difference interpolation method is used during the iterative process for estimating the guessing values. The properties including the order, zerostable and stability region of the proposed method are discussed. Numerical examples are given to demonstrate the computational efficiency of the developed method. |
| first_indexed | 2025-11-15T03:06:02Z |
| format | Article |
| id | ump-32341 |
| institution | Universiti Malaysia Pahang |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T03:06:02Z |
| publishDate | 2019 |
| publisher | Akademi Sains Malaysia |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | ump-323412021-11-05T07:36:30Z http://umpir.ump.edu.my/id/eprint/32341/ Two-point diagonally implicit multistep block method for solving Robin boundary value problems using variable step size strategy Nadirah, Mohd Nasir Zanariah, Abdul Majid Fudziah, Ismail Norfifah, Bachok QA Mathematics This study focuses on the multistep integration method for approximating directly the solutions of the second order boundary value problems (BVPs) with Robin boundary conditions. The derivation of the predictor and corrector formulas uses Lagrange interpolation polynomial in the form of Adam's method. Two numerical solutions are computed concurrently within a block method with non-uniformly step size. The implementation of multistep block method follows the m PE(CE) procedure via shooting technique. Newton divided difference interpolation method is used during the iterative process for estimating the guessing values. The properties including the order, zerostable and stability region of the proposed method are discussed. Numerical examples are given to demonstrate the computational efficiency of the developed method. Akademi Sains Malaysia 2019 Article PeerReviewed pdf en http://umpir.ump.edu.my/id/eprint/32341/1/PAPER%202.pdf Nadirah, Mohd Nasir and Zanariah, Abdul Majid and Fudziah, Ismail and Norfifah, Bachok (2019) Two-point diagonally implicit multistep block method for solving Robin boundary value problems using variable step size strategy. ASM Science Journal, 12 (Spe. Issue 5). pp. 10-16. ISSN 1823-6782. (Published) https://www.akademisains.gov.my/asmsj/?mdocs-file=4149 |
| spellingShingle | QA Mathematics Nadirah, Mohd Nasir Zanariah, Abdul Majid Fudziah, Ismail Norfifah, Bachok Two-point diagonally implicit multistep block method for solving Robin boundary value problems using variable step size strategy |
| title | Two-point diagonally implicit multistep block method for solving Robin boundary value problems using variable step size strategy |
| title_full | Two-point diagonally implicit multistep block method for solving Robin boundary value problems using variable step size strategy |
| title_fullStr | Two-point diagonally implicit multistep block method for solving Robin boundary value problems using variable step size strategy |
| title_full_unstemmed | Two-point diagonally implicit multistep block method for solving Robin boundary value problems using variable step size strategy |
| title_short | Two-point diagonally implicit multistep block method for solving Robin boundary value problems using variable step size strategy |
| title_sort | two-point diagonally implicit multistep block method for solving robin boundary value problems using variable step size strategy |
| topic | QA Mathematics |
| url | http://umpir.ump.edu.my/id/eprint/32341/ http://umpir.ump.edu.my/id/eprint/32341/ http://umpir.ump.edu.my/id/eprint/32341/1/PAPER%202.pdf |