Block one-step methods for solving stiff differential equations
In this research, both stiff ordinary differential equations (ODEs) and parabolic partial differential equation (PDEs) are solved using the A-stable one-step block method with Newton’s iteration with constant step size. Two-point block one-step method and three-point block one-step method had bee...
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| Format: | Thesis |
| Language: | English |
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2014
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| Online Access: | http://psasir.upm.edu.my/id/eprint/76038/ http://psasir.upm.edu.my/id/eprint/76038/1/IPM%202014%2011.pdf |
| _version_ | 1848857854878941184 |
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| author | Mohd Zabidi, Muhammad Izzat Zakwan |
| author_facet | Mohd Zabidi, Muhammad Izzat Zakwan |
| author_sort | Mohd Zabidi, Muhammad Izzat Zakwan |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | In this research, both stiff ordinary differential equations (ODEs) and parabolic partial
differential equation (PDEs) are solved using the A-stable one-step block method with
Newton’s iteration with constant step size.
Two-point block one-step method and three-point block one-step method had been
proposed in this research. These two methods are used to approximate the solutions for
stiff ODEs and parabolic PDEs at two and three points simultaneously. The
implementation of these methods will be in predictor and corrector mode. The predictor
formulae is formulated from the modified block method itself. Newton’s iteration is
adapted in implementation of the block methods. The order, error constant, convergence
and stability of each method are also discussed.
This study also focused on solving parabolic PDEs. In order to solve parabolic PDEs
using the proposed methods, we reduced the form of parabolic PDEs into ODEs by
discretizing the parabolic equation using method of line. To illustrate the applicability of
the proposed method, several numerical results are shown and compared with the results
obtained by the existing methods
In conclusion, the proposed methods are suitable for solving stiff ordinary differential
equations at varies stepsizes especially when the stepsizes are larger. Other than that, the
proposed method also appropriate for solving stiff parabolic partial differential equations
due to acceptable results that had been produced. |
| first_indexed | 2025-11-15T12:04:10Z |
| format | Thesis |
| id | upm-76038 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T12:04:10Z |
| publishDate | 2014 |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-760382025-06-18T02:36:34Z http://psasir.upm.edu.my/id/eprint/76038/ Block one-step methods for solving stiff differential equations Mohd Zabidi, Muhammad Izzat Zakwan In this research, both stiff ordinary differential equations (ODEs) and parabolic partial differential equation (PDEs) are solved using the A-stable one-step block method with Newton’s iteration with constant step size. Two-point block one-step method and three-point block one-step method had been proposed in this research. These two methods are used to approximate the solutions for stiff ODEs and parabolic PDEs at two and three points simultaneously. The implementation of these methods will be in predictor and corrector mode. The predictor formulae is formulated from the modified block method itself. Newton’s iteration is adapted in implementation of the block methods. The order, error constant, convergence and stability of each method are also discussed. This study also focused on solving parabolic PDEs. In order to solve parabolic PDEs using the proposed methods, we reduced the form of parabolic PDEs into ODEs by discretizing the parabolic equation using method of line. To illustrate the applicability of the proposed method, several numerical results are shown and compared with the results obtained by the existing methods In conclusion, the proposed methods are suitable for solving stiff ordinary differential equations at varies stepsizes especially when the stepsizes are larger. Other than that, the proposed method also appropriate for solving stiff parabolic partial differential equations due to acceptable results that had been produced. 2014-09 Thesis NonPeerReviewed text en http://psasir.upm.edu.my/id/eprint/76038/1/IPM%202014%2011.pdf Mohd Zabidi, Muhammad Izzat Zakwan (2014) Block one-step methods for solving stiff differential equations. Masters thesis, Universiti Putra Malaysia. http://ethesis.upm.edu.my/id/eprint/13120/ Differential equations - Numerical solutions Stiff computation (Differential equations) |
| spellingShingle | Differential equations - Numerical solutions Stiff computation (Differential equations) Mohd Zabidi, Muhammad Izzat Zakwan Block one-step methods for solving stiff differential equations |
| title | Block one-step methods for solving stiff differential equations |
| title_full | Block one-step methods for solving stiff differential equations |
| title_fullStr | Block one-step methods for solving stiff differential equations |
| title_full_unstemmed | Block one-step methods for solving stiff differential equations |
| title_short | Block one-step methods for solving stiff differential equations |
| title_sort | block one-step methods for solving stiff differential equations |
| topic | Differential equations - Numerical solutions Stiff computation (Differential equations) |
| url | http://psasir.upm.edu.my/id/eprint/76038/ http://psasir.upm.edu.my/id/eprint/76038/ http://psasir.upm.edu.my/id/eprint/76038/1/IPM%202014%2011.pdf |