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A Solution of the Complex Fuzzy Heat Equation in Terms of Complex Dirichlet Conditions Using a Modified Crank–Nicolson Method

Author

Listed:
  • Hamzeh Zureigat
  • Mohammad A. Tashtoush
  • Ali F. Al Jassar
  • Emad A. Az-Zo’bi
  • Mohammad W. Alomari

Abstract

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.

Suggested Citation

  • Hamzeh Zureigat & Mohammad A. Tashtoush & Ali F. Al Jassar & Emad A. Az-Zo’bi & Mohammad W. Alomari, 2023. "A Solution of the Complex Fuzzy Heat Equation in Terms of Complex Dirichlet Conditions Using a Modified Crank–Nicolson Method," Advances in Mathematical Physics, John Wiley & Sons, vol. 2023(1).
    • Handle: RePEc:wly:jnlamp:v:2023:y:2023:i:1:n:6505227
    DOI: 10.1155/2023/6505227
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    References listed on IDEAS

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    1. Maryam Almutairi & Hamzeh Zureigat & Ahmad Izani Ismail & Ali Fareed Jameel, 2021. "Fuzzy Numerical Solution via Finite Difference Scheme of Wave Equation in Double Parametrical Fuzzy Number Form," Mathematics, MDPI, vol. 9(6), pages 1-16, March.
    2. Al-Smadi, Mohammed & Arqub, Omar Abu & Zeidan, Dia, 2021. "Fuzzy fractional differential equations under the Mittag-Leffler kernel differential operator of the ABC approach: Theorems and applications," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    3. Abd Ulazeez M. Alkouri & Abdul Razak Salleh, 2013. "Complex Atanassov′s Intuitionistic Fuzzy Relation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    4. Moiseis S. Cecconello & Jefferson Leite & Rodney C. Bassanezi & Joao de Deus M. Silva, 2013. "About Projections of Solutions for Fuzzy Differential Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    5. Hasan, Shatha & Al-Smadi, Mohammed & El-Ajou, Ahmad & Momani, Shaher & Hadid, Samir & Al-Zhour, Zeyad, 2021. "Numerical approach in the Hilbert space to solve a fuzzy Atangana-Baleanu fractional hybrid system," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    6. Abd Ulazeez M. Alkouri & Abdul Razak Salleh, 2013. "Complex Atanassov's Intuitionistic Fuzzy Relation," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-18, June.
    7. Moiseis S. Cecconello & Jefferson Leite & Rodney C. Bassanezi & Joao de Deus M. Silva, 2013. "About Projections of Solutions for Fuzzy Differential Equations," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-9, June.
    8. Alessandra Jannelli, 2020. "Numerical Solutions of Fractional Differential Equations Arising in Engineering Sciences," Mathematics, MDPI, vol. 8(2), pages 1-14, February.
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