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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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Main Authors: Rahimah, Jusoh, Aksah, Saufianim J., Nooraini, Zainuddin, Zarina, Ibrahim
Format: Article
Language:English
Published: International Association of Engineers 2023
Subjects:
QA Mathematics
Online Access:http://umpir.ump.edu.my/id/eprint/39861/1/Numerical%20Solver%20of%20alpha-Stable%20for%20Stiff%20Ordinary%20Differential%20Equations.pdf
http://umpir.ump.edu.my/id/eprint/39861/
https://www.engineeringletters.com/issues_v31/issue_4/EL_31_4_28.pdf
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spelling my.ump.umpir.398612024-01-04T07:05:59Z 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
institution Universiti Malaysia Pahang Al-Sultan Abdullah
building UMPSA Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Malaysia Pahang Al-Sultan Abdullah
content_source UMPSA Institutional Repository
url_provider http://umpir.ump.edu.my/
language English
topic QA Mathematics
spellingShingle QA Mathematics
Rahimah, Jusoh
Aksah, Saufianim J.
Nooraini, Zainuddin
Zarina, Ibrahim
Numerical solver of A(alpha)-stable for stiff ordinary differential equations
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.
format Article
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
title 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_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_sort numerical solver of a(alpha)-stable for stiff ordinary differential equations
publisher International Association of Engineers
publishDate 2023
url http://umpir.ump.edu.my/id/eprint/39861/1/Numerical%20Solver%20of%20alpha-Stable%20for%20Stiff%20Ordinary%20Differential%20Equations.pdf
http://umpir.ump.edu.my/id/eprint/39861/
https://www.engineeringletters.com/issues_v31/issue_4/EL_31_4_28.pdf
_version_ 1822924030002331648
score 13.244413

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