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Numerical Solution for Fuzzy Diffusion Problem via Two Parameter Alternating Group Explicit Technique

The computational technique has become a significant area of study in physics and engineering. The first method to evaluate the problems numerically was a finite difference. In 2002, a computational approach, an explicit finite difference technique, was used to overcome the fuzzy partial differentia...

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Main Authors: A. A. Dahalan, Jumat Sulaiman
Format: Article
Language:English
English
Published: Horizon Research Publishing 2021
Subjects:
QC1-999 Physics
T1-995 Technology (General)
Online Access:https://eprints.ums.edu.my/id/eprint/36478/1/ABSTRACT.pdf
https://eprints.ums.edu.my/id/eprint/36478/2/FULL%20TEXT.pdf
https://eprints.ums.edu.my/id/eprint/36478/
http://dx.doi.org/10.13189/ms.2021.090203
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spelling my.ums.eprints.364782024-01-19T02:54:40Z https://eprints.ums.edu.my/id/eprint/36478/ Numerical Solution for Fuzzy Diffusion Problem via Two Parameter Alternating Group Explicit Technique A. A. Dahalan Jumat Sulaiman QC1-999 Physics T1-995 Technology (General) The computational technique has become a significant area of study in physics and engineering. The first method to evaluate the problems numerically was a finite difference. In 2002, a computational approach, an explicit finite difference technique, was used to overcome the fuzzy partial differential equation (FPDE) based on the Seikkala derivative. The application of the iterative technique, in particular the Two Parameter Alternating Group Explicit (TAGE) method, is employed to resolve the finite difference approximation resulting after the fuzzy heat equation is investigated in this article. This article broadens the use of the TAGE iterative technique to solve fuzzy problems due to the reliability of the approaches. The development and execution of the TAGE technique towards the full-sweep (FS) and half-sweep (HS) techniques are also presented. The idea of using the HS scheme is to reduce the computational complexity of the iterative methods by nearly/more than half. Additionally, numerical outcomes from the solution of two experimental problems are included and compared with the Alternating Group Explicit (AGE) approaches to clarify their feasibility. In conclusion, the families of the TAGE technique have been used to overcome the linear system structure through a one-dimensional fuzzy diffusion (1D-FD) discretization using a finite difference scheme. The findings suggest that the HSTAGE approach is surpassing in terms of iteration counts, time taken, and Hausdorff distance relative to the FSTAGE and AGE approaches. It demonstrates that the number of iterations for HSTAGE approach has decreased by approximately 71.60-72.95%, whereas for the execution time, the implementation of HSTAGE method is between 74.05-86.42% better. Since TAGE is ideal for concurrent processing, this method has been seen as the key benefit as it consumes sets of independent tasks that can be performed at the same time. The ability of the suggested technique is projected to be useful for the advanced exploration in solving any multi-dimensional FPDEs. Horizon Research Publishing 2021-12 Article NonPeerReviewed text en https://eprints.ums.edu.my/id/eprint/36478/1/ABSTRACT.pdf text en https://eprints.ums.edu.my/id/eprint/36478/2/FULL%20TEXT.pdf A. A. Dahalan and Jumat Sulaiman (2021) Numerical Solution for Fuzzy Diffusion Problem via Two Parameter Alternating Group Explicit Technique. Mathematics and Statistics, 9. pp. 98-105. ISSN 2332-2071 http://dx.doi.org/10.13189/ms.2021.090203
institution Universiti Malaysia Sabah
building UMS Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Malaysia Sabah
content_source UMS Institutional Repository
url_provider http://eprints.ums.edu.my/
language English
English
topic QC1-999 Physics
T1-995 Technology (General)
spellingShingle QC1-999 Physics
T1-995 Technology (General)
A. A. Dahalan
Jumat Sulaiman
Numerical Solution for Fuzzy Diffusion Problem via Two Parameter Alternating Group Explicit Technique
description The computational technique has become a significant area of study in physics and engineering. The first method to evaluate the problems numerically was a finite difference. In 2002, a computational approach, an explicit finite difference technique, was used to overcome the fuzzy partial differential equation (FPDE) based on the Seikkala derivative. The application of the iterative technique, in particular the Two Parameter Alternating Group Explicit (TAGE) method, is employed to resolve the finite difference approximation resulting after the fuzzy heat equation is investigated in this article. This article broadens the use of the TAGE iterative technique to solve fuzzy problems due to the reliability of the approaches. The development and execution of the TAGE technique towards the full-sweep (FS) and half-sweep (HS) techniques are also presented. The idea of using the HS scheme is to reduce the computational complexity of the iterative methods by nearly/more than half. Additionally, numerical outcomes from the solution of two experimental problems are included and compared with the Alternating Group Explicit (AGE) approaches to clarify their feasibility. In conclusion, the families of the TAGE technique have been used to overcome the linear system structure through a one-dimensional fuzzy diffusion (1D-FD) discretization using a finite difference scheme. The findings suggest that the HSTAGE approach is surpassing in terms of iteration counts, time taken, and Hausdorff distance relative to the FSTAGE and AGE approaches. It demonstrates that the number of iterations for HSTAGE approach has decreased by approximately 71.60-72.95%, whereas for the execution time, the implementation of HSTAGE method is between 74.05-86.42% better. Since TAGE is ideal for concurrent processing, this method has been seen as the key benefit as it consumes sets of independent tasks that can be performed at the same time. The ability of the suggested technique is projected to be useful for the advanced exploration in solving any multi-dimensional FPDEs.
format Article
author A. A. Dahalan
Jumat Sulaiman
author_facet A. A. Dahalan
Jumat Sulaiman
author_sort A. A. Dahalan
title Numerical Solution for Fuzzy Diffusion Problem via Two Parameter Alternating Group Explicit Technique
title_short Numerical Solution for Fuzzy Diffusion Problem via Two Parameter Alternating Group Explicit Technique
title_full Numerical Solution for Fuzzy Diffusion Problem via Two Parameter Alternating Group Explicit Technique
title_fullStr Numerical Solution for Fuzzy Diffusion Problem via Two Parameter Alternating Group Explicit Technique
title_full_unstemmed Numerical Solution for Fuzzy Diffusion Problem via Two Parameter Alternating Group Explicit Technique
title_sort numerical solution for fuzzy diffusion problem via two parameter alternating group explicit technique
publisher Horizon Research Publishing
publishDate 2021
url https://eprints.ums.edu.my/id/eprint/36478/1/ABSTRACT.pdf
https://eprints.ums.edu.my/id/eprint/36478/2/FULL%20TEXT.pdf
https://eprints.ums.edu.my/id/eprint/36478/
http://dx.doi.org/10.13189/ms.2021.090203
_version_ 1789425994392666112
score 13.211869

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