A Solution of the Complex Fuzzy Heat Equation in Terms of Complex Dirichlet Conditions Using a Modified Crank–Nicolson Method
Complex fuzzy sets (CFSs) have recently emerged as a potent tool for expanding the scope of fuzzy sets to encompass wider ranges within the unit disk in the complex plane. This study explores complex fuzzy numbers and introduces their application for the first time in the literature to address a com...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2023-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2023/6505227 |
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| author | Hamzeh Zureigat Mohammad A. Tashtoush Ali F. Al Jassar Emad A. Az-Zo’bi Mohammad W. Alomari |
| author_facet | Hamzeh Zureigat Mohammad A. Tashtoush Ali F. Al Jassar Emad A. Az-Zo’bi Mohammad W. Alomari |
| author_sort | Hamzeh Zureigat |
| collection | DOAJ |
| description | Complex fuzzy sets (CFSs) have recently emerged as a potent tool for expanding the scope of fuzzy sets to encompass wider ranges within the unit disk in the complex plane. This study explores complex fuzzy numbers and introduces their application for the first time in the literature to address a complex fuzzy partial differential equation that involves a complex fuzzy heat equation under Hukuhara differentiability. The researchers utilize an implicit finite difference scheme, namely the Crank–Nicolson method, to tackle complex fuzzy heat equations. The problem’s fuzziness arises from the coefficients in both amplitude and phase terms, as well as in the initial and boundary conditions, with the Convex normalized triangular fuzzy numbers extended to the unit disk in the complex plane. The researchers take advantage of the properties and benefits of CFS theory in the proposed numerical methods and subsequently provide a new proof of the stability under CFS theory. A numerical example is presented to demonstrate the proposed approach’s reliability and feasibility, with the results showing good agreement with the exact solution and relevant theoretical aspects. |
| format | Article |
| id | doaj-art-873a470617134a6499b67ec8089383ac |
| institution | Kabale University |
| issn | 1687-9139 |
| language | English |
| publishDate | 2023-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-873a470617134a6499b67ec8089383ac2025-02-03T06:43:15ZengWileyAdvances in Mathematical Physics1687-91392023-01-01202310.1155/2023/6505227A Solution of the Complex Fuzzy Heat Equation in Terms of Complex Dirichlet Conditions Using a Modified Crank–Nicolson MethodHamzeh Zureigat0Mohammad A. Tashtoush1Ali F. Al Jassar2Emad A. Az-Zo’bi3Mohammad W. Alomari4Department of MathematicsFaculty of Education and ArtsFaculty of Education and ArtsDepartment of MathematicsDepartment of MathematicsComplex fuzzy sets (CFSs) have recently emerged as a potent tool for expanding the scope of fuzzy sets to encompass wider ranges within the unit disk in the complex plane. This study explores complex fuzzy numbers and introduces their application for the first time in the literature to address a complex fuzzy partial differential equation that involves a complex fuzzy heat equation under Hukuhara differentiability. The researchers utilize an implicit finite difference scheme, namely the Crank–Nicolson method, to tackle complex fuzzy heat equations. The problem’s fuzziness arises from the coefficients in both amplitude and phase terms, as well as in the initial and boundary conditions, with the Convex normalized triangular fuzzy numbers extended to the unit disk in the complex plane. The researchers take advantage of the properties and benefits of CFS theory in the proposed numerical methods and subsequently provide a new proof of the stability under CFS theory. A numerical example is presented to demonstrate the proposed approach’s reliability and feasibility, with the results showing good agreement with the exact solution and relevant theoretical aspects.http://dx.doi.org/10.1155/2023/6505227 |
| spellingShingle | Hamzeh Zureigat Mohammad A. Tashtoush Ali F. Al Jassar Emad A. Az-Zo’bi Mohammad W. Alomari A Solution of the Complex Fuzzy Heat Equation in Terms of Complex Dirichlet Conditions Using a Modified Crank–Nicolson Method Advances in Mathematical Physics |
| title | A Solution of the Complex Fuzzy Heat Equation in Terms of Complex Dirichlet Conditions Using a Modified Crank–Nicolson Method |
| title_full | A Solution of the Complex Fuzzy Heat Equation in Terms of Complex Dirichlet Conditions Using a Modified Crank–Nicolson Method |
| title_fullStr | A Solution of the Complex Fuzzy Heat Equation in Terms of Complex Dirichlet Conditions Using a Modified Crank–Nicolson Method |
| title_full_unstemmed | A Solution of the Complex Fuzzy Heat Equation in Terms of Complex Dirichlet Conditions Using a Modified Crank–Nicolson Method |
| title_short | A Solution of the Complex Fuzzy Heat Equation in Terms of Complex Dirichlet Conditions Using a Modified Crank–Nicolson Method |
| title_sort | solution of the complex fuzzy heat equation in terms of complex dirichlet conditions using a modified crank nicolson method |
| url | http://dx.doi.org/10.1155/2023/6505227 |
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