Numerical solver of A(alpha)-stable for stiff ordinary differential equations
In this paper, a numerical solver for stiff ordinary differential equations (ODEs) known as the Extended Singly Diagonally Implicit Block Backward Differentiation Formulas (ESDIBDDF) is developed. Objectives of this study are to analyse the A( ) − stability of the ESDIBBDF method and enhance its a...
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| Format: | Article |
| Language: | English |
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International Association of Engineers
2023
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| Online Access: | http://umpir.ump.edu.my/id/eprint/39861/1/Numerical%20Solver%20of%20alpha-Stable%20for%20Stiff%20Ordinary%20Differential%20Equations.pdf |
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| author | Rahimah, Jusoh Aksah, Saufianim J. Nooraini, Zainuddin Zarina, Ibrahim |
| author_facet | Rahimah, Jusoh Aksah, Saufianim J. Nooraini, Zainuddin Zarina, Ibrahim |
| author_sort | Rahimah, Jusoh |
| collection | UMP |
| description | In this paper, a numerical solver for stiff ordinary differential equations (ODEs) known as the Extended Singly Diagonally Implicit Block Backward Differentiation Formulas (ESDIBDDF) is developed. Objectives of this study are to analyse the A( ) − stability of the ESDIBBDF method and enhance its accuracy by employing a strategy that minimizes the error norm to optimize the values of free parameters. In addition to that, accuracy of the method is to be enhanced by approximating solutions by implementing extra functions to be evaluated. The formula is specifically designed in a lower triangular form with equal diagonal coefficients, enabling faster computation of numerical solutions. Numerical experiments are conducted to assess the efficiency of this method as a solver for stiff ODEs, comparing it with existing methods. The A( ) − stability analysis is verified and conditions for convergence are discussed. The conclusive works efficiently as an alternate solver for stiff ODEs. The research recommended extended application of the developed method to solve applied problems. |
| first_indexed | 2024-03-06T13:12:34Z |
| format | Article |
| id | UMPir39861 |
| institution | Universiti Malaysia Pahang |
| language | English |
| last_indexed | 2024-03-06T13:12:34Z |
| publishDate | 2023 |
| publisher | International Association of Engineers |
| record_format | dspace |
| spelling | UMPir398612024-01-04T07:05:59Z http://umpir.ump.edu.my/id/eprint/39861/ Numerical solver of A(alpha)-stable for stiff ordinary differential equations Rahimah, Jusoh Aksah, Saufianim J. Nooraini, Zainuddin Zarina, Ibrahim QA Mathematics In this paper, a numerical solver for stiff ordinary differential equations (ODEs) known as the Extended Singly Diagonally Implicit Block Backward Differentiation Formulas (ESDIBDDF) is developed. Objectives of this study are to analyse the A( ) − stability of the ESDIBBDF method and enhance its accuracy by employing a strategy that minimizes the error norm to optimize the values of free parameters. In addition to that, accuracy of the method is to be enhanced by approximating solutions by implementing extra functions to be evaluated. The formula is specifically designed in a lower triangular form with equal diagonal coefficients, enabling faster computation of numerical solutions. Numerical experiments are conducted to assess the efficiency of this method as a solver for stiff ODEs, comparing it with existing methods. The A( ) − stability analysis is verified and conditions for convergence are discussed. The conclusive works efficiently as an alternate solver for stiff ODEs. The research recommended extended application of the developed method to solve applied problems. International Association of Engineers 2023-11 Article PeerReviewed pdf en cc_by_nc_nd_4 http://umpir.ump.edu.my/id/eprint/39861/1/Numerical%20Solver%20of%20alpha-Stable%20for%20Stiff%20Ordinary%20Differential%20Equations.pdf Rahimah, Jusoh and Aksah, Saufianim J. and Nooraini, Zainuddin and Zarina, Ibrahim (2023) Numerical solver of A(alpha)-stable for stiff ordinary differential equations. Engineering Letters, 31 (4). pp. 1574-1583. ISSN 1816-093X (Print); 1816-0948 (Online). (Published) https://www.engineeringletters.com/issues_v31/issue_4/EL_31_4_28.pdf |
| spellingShingle | QA Mathematics Rahimah, Jusoh Aksah, Saufianim J. Nooraini, Zainuddin Zarina, Ibrahim Numerical solver of A(alpha)-stable for stiff ordinary differential equations |
| title | Numerical solver of A(alpha)-stable for stiff ordinary differential equations |
| title_full | Numerical solver of A(alpha)-stable for stiff ordinary differential equations |
| title_fullStr | Numerical solver of A(alpha)-stable for stiff ordinary differential equations |
| title_full_unstemmed | Numerical solver of A(alpha)-stable for stiff ordinary differential equations |
| title_short | Numerical solver of A(alpha)-stable for stiff ordinary differential equations |
| title_sort | numerical solver of a alpha stable for stiff ordinary differential equations |
| topic | QA Mathematics |
| url | http://umpir.ump.edu.my/id/eprint/39861/1/Numerical%20Solver%20of%20alpha-Stable%20for%20Stiff%20Ordinary%20Differential%20Equations.pdf |
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