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Formulation of a new implicit method for group implicit BBDF in solving related stiff ordinary differential equations

This paper proposed a new alternative approach of the implicit diagonal block backward differentiation formula (BBDF) to solve linear and nonlinear first-order stiff ordinary differential equations (ODEs). We generate the solver by manipulating the numbers of back values to achieve a higher-order po...

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Main Authors: Abd Rasid, Norshakila, Ibrahim, Zarina Bibi, Abdul Majid, Zanariah, Ismail, Fudziah
Format: Article
Language:English
Published: Horizon Research Publishing 2021
Online Access:http://psasir.upm.edu.my/id/eprint/97386/1/ABSTRACT.pdf
http://psasir.upm.edu.my/id/eprint/97386/
https://www.hrpub.org/journals/article_info.php?aid=10708
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spelling my.upm.eprints.973862022-09-05T08:46:30Z http://psasir.upm.edu.my/id/eprint/97386/ Formulation of a new implicit method for group implicit BBDF in solving related stiff ordinary differential equations Abd Rasid, Norshakila Ibrahim, Zarina Bibi Abdul Majid, Zanariah Ismail, Fudziah This paper proposed a new alternative approach of the implicit diagonal block backward differentiation formula (BBDF) to solve linear and nonlinear first-order stiff ordinary differential equations (ODEs). We generate the solver by manipulating the numbers of back values to achieve a higher-order possible using the interpolation procedure. The algorithm is developed and implemented in C ++ medium. The numerical integrator approximates few solution points concurrently with off-step points in a block scheme over a non-overlapping solution interval at a single iteration. The lower triangular matrix form of the implicit diagonal causes fewer differentiation coefficients and ultimately reduces the execution time during running codes. We choose two intermediate points as off-step points appropriately, which are proven to guarantee the method's zero stability. The off-step points help to increase the accuracy by optimizing the local truncation error. The proposed solver satisfied theoretical consistency and zero-stable requirements, leading to a convergent multistep method with third algebraic order. We used the well-known and standard linear and nonlinear stiff IVP problems used in literature for validation to measure the algorithm's accuracy and processor time efficiency. The performance metrics are validated by comparing them with a proven solver, and the output shows that the alternative method is better than the existing one. Horizon Research Publishing 2021 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/97386/1/ABSTRACT.pdf Abd Rasid, Norshakila and Ibrahim, Zarina Bibi and Abdul Majid, Zanariah and Ismail, Fudziah (2021) Formulation of a new implicit method for group implicit BBDF in solving related stiff ordinary differential equations. Mathematics and Statistics, 9 (2). 144 - 150. ISSN 2332-2071; ESSN: 2332-2144 https://www.hrpub.org/journals/article_info.php?aid=10708 10.13189/ms.2021.090208
institution Universiti Putra Malaysia
building UPM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Putra Malaysia
content_source UPM Institutional Repository
url_provider http://psasir.upm.edu.my/
language English
description This paper proposed a new alternative approach of the implicit diagonal block backward differentiation formula (BBDF) to solve linear and nonlinear first-order stiff ordinary differential equations (ODEs). We generate the solver by manipulating the numbers of back values to achieve a higher-order possible using the interpolation procedure. The algorithm is developed and implemented in C ++ medium. The numerical integrator approximates few solution points concurrently with off-step points in a block scheme over a non-overlapping solution interval at a single iteration. The lower triangular matrix form of the implicit diagonal causes fewer differentiation coefficients and ultimately reduces the execution time during running codes. We choose two intermediate points as off-step points appropriately, which are proven to guarantee the method's zero stability. The off-step points help to increase the accuracy by optimizing the local truncation error. The proposed solver satisfied theoretical consistency and zero-stable requirements, leading to a convergent multistep method with third algebraic order. We used the well-known and standard linear and nonlinear stiff IVP problems used in literature for validation to measure the algorithm's accuracy and processor time efficiency. The performance metrics are validated by comparing them with a proven solver, and the output shows that the alternative method is better than the existing one.
format Article
author Abd Rasid, Norshakila
Ibrahim, Zarina Bibi
Abdul Majid, Zanariah
Ismail, Fudziah
spellingShingle Abd Rasid, Norshakila
Ibrahim, Zarina Bibi
Abdul Majid, Zanariah
Ismail, Fudziah
Formulation of a new implicit method for group implicit BBDF in solving related stiff ordinary differential equations
author_facet Abd Rasid, Norshakila
Ibrahim, Zarina Bibi
Abdul Majid, Zanariah
Ismail, Fudziah
author_sort Abd Rasid, Norshakila
title Formulation of a new implicit method for group implicit BBDF in solving related stiff ordinary differential equations
title_short Formulation of a new implicit method for group implicit BBDF in solving related stiff ordinary differential equations
title_full Formulation of a new implicit method for group implicit BBDF in solving related stiff ordinary differential equations
title_fullStr Formulation of a new implicit method for group implicit BBDF in solving related stiff ordinary differential equations
title_full_unstemmed Formulation of a new implicit method for group implicit BBDF in solving related stiff ordinary differential equations
title_sort formulation of a new implicit method for group implicit bbdf in solving related stiff ordinary differential equations
publisher Horizon Research Publishing
publishDate 2021
url http://psasir.upm.edu.my/id/eprint/97386/1/ABSTRACT.pdf
http://psasir.upm.edu.my/id/eprint/97386/
https://www.hrpub.org/journals/article_info.php?aid=10708
_version_ 1744355329020264448
score 13.211869

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