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Diagonally implicit multistep block method of order four for solving fuzzy differential equations using Seikkala derivatives

In this paper, the solution of fuzzy differential equations is approximated numerically using diagonally implicit multistep block method of order four. The multistep block method is well known as an efficient and accurate method for solving ordinary differential equations, hence in this paper the me...

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Main Authors: Isa, Syahirbanun, Abdul Majid, Zanariah, Ismail, Fudziah, Rabiei, Faranak
Format: Article
Language:English
Published: MDPI 2018
Subjects:
QA299.6-433 Analysis
T57-57.97 Applied mathematics. Quantitative methods
Online Access:http://eprints.uthm.edu.my/5501/1/AJ%202018%20%28868%29%20Diagonally%20implicit%20multistep%20block%20method%20of%20order%20four%20for%20solving%20fuzzy%20differential%20equations%20using%20Seikkala%20derivatives..pdf
http://eprints.uthm.edu.my/5501/
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spelling my.uthm.eprints.55012022-01-13T01:38:09Z http://eprints.uthm.edu.my/5501/ Diagonally implicit multistep block method of order four for solving fuzzy differential equations using Seikkala derivatives Isa, Syahirbanun Abdul Majid, Zanariah Ismail, Fudziah Rabiei, Faranak QA299.6-433 Analysis T57-57.97 Applied mathematics. Quantitative methods In this paper, the solution of fuzzy differential equations is approximated numerically using diagonally implicit multistep block method of order four. The multistep block method is well known as an efficient and accurate method for solving ordinary differential equations, hence in this paper the method will be used to solve the fuzzy initial value problems where the initial value is a symmetric triangular fuzzy interval. The triangular fuzzy number is not necessarily symmetric, however by imposing symmetry the definition of a triangular fuzzy number can be simplified. The symmetric triangular fuzzy interval is a triangular fuzzy interval that has same left and right width of membership function from the center. Due to this, the parametric form of symmetric triangular fuzzy number is simple and the performing arithmetic operations become easier. In order to interpret the fuzzy problems, Seikkala’s derivative approach is implemented. Characterization theorem is then used to translate the problems into a system of ordinary differential equations. The convergence of the introduced method is also proved. Numerical examples are given to investigate the performance of the proposed method. It is clearly shown in the results that the proposed method is comparable and reliable in solving fuzzy differential equations. MDPI 2018 Article PeerReviewed text en http://eprints.uthm.edu.my/5501/1/AJ%202018%20%28868%29%20Diagonally%20implicit%20multistep%20block%20method%20of%20order%20four%20for%20solving%20fuzzy%20differential%20equations%20using%20Seikkala%20derivatives..pdf Isa, Syahirbanun and Abdul Majid, Zanariah and Ismail, Fudziah and Rabiei, Faranak (2018) Diagonally implicit multistep block method of order four for solving fuzzy differential equations using Seikkala derivatives. Symmetry, 10 (42). pp. 1-21. ISSN 2073-8994
institution Universiti Tun Hussein Onn Malaysia
building UTHM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Tun Hussein Onn Malaysia
content_source UTHM Institutional Repository
url_provider http://eprints.uthm.edu.my/
language English
topic QA299.6-433 Analysis
T57-57.97 Applied mathematics. Quantitative methods
spellingShingle QA299.6-433 Analysis
T57-57.97 Applied mathematics. Quantitative methods
Isa, Syahirbanun
Abdul Majid, Zanariah
Ismail, Fudziah
Rabiei, Faranak
Diagonally implicit multistep block method of order four for solving fuzzy differential equations using Seikkala derivatives
description In this paper, the solution of fuzzy differential equations is approximated numerically using diagonally implicit multistep block method of order four. The multistep block method is well known as an efficient and accurate method for solving ordinary differential equations, hence in this paper the method will be used to solve the fuzzy initial value problems where the initial value is a symmetric triangular fuzzy interval. The triangular fuzzy number is not necessarily symmetric, however by imposing symmetry the definition of a triangular fuzzy number can be simplified. The symmetric triangular fuzzy interval is a triangular fuzzy interval that has same left and right width of membership function from the center. Due to this, the parametric form of symmetric triangular fuzzy number is simple and the performing arithmetic operations become easier. In order to interpret the fuzzy problems, Seikkala’s derivative approach is implemented. Characterization theorem is then used to translate the problems into a system of ordinary differential equations. The convergence of the introduced method is also proved. Numerical examples are given to investigate the performance of the proposed method. It is clearly shown in the results that the proposed method is comparable and reliable in solving fuzzy differential equations.
format Article
author Isa, Syahirbanun
Abdul Majid, Zanariah
Ismail, Fudziah
Rabiei, Faranak
author_facet Isa, Syahirbanun
Abdul Majid, Zanariah
Ismail, Fudziah
Rabiei, Faranak
author_sort Isa, Syahirbanun
title Diagonally implicit multistep block method of order four for solving fuzzy differential equations using Seikkala derivatives
title_short Diagonally implicit multistep block method of order four for solving fuzzy differential equations using Seikkala derivatives
title_full Diagonally implicit multistep block method of order four for solving fuzzy differential equations using Seikkala derivatives
title_fullStr Diagonally implicit multistep block method of order four for solving fuzzy differential equations using Seikkala derivatives
title_full_unstemmed Diagonally implicit multistep block method of order four for solving fuzzy differential equations using Seikkala derivatives
title_sort diagonally implicit multistep block method of order four for solving fuzzy differential equations using seikkala derivatives
publisher MDPI
publishDate 2018
url http://eprints.uthm.edu.my/5501/1/AJ%202018%20%28868%29%20Diagonally%20implicit%20multistep%20block%20method%20of%20order%20four%20for%20solving%20fuzzy%20differential%20equations%20using%20Seikkala%20derivatives..pdf
http://eprints.uthm.edu.my/5501/
_version_ 1738581385254273024
score 13.211869

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