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Double Parametric Fuzzy Numbers Approximate Scheme for Solving One-Dimensional Fuzzy Heat-Like and Wave-Like Equations

Author

Listed:
  • Ali Fareed Jameel

    (School of Quantitative Sciences, College of Arts and Sciences, Universiti Utara Malaysia (UUM), Sintok, Kedah 06010, Malaysia)

  • Sarmad A. Jameel Altaie

    (School of Quantitative Sciences, College of Arts and Sciences, Universiti Utara Malaysia (UUM), Sintok, Kedah 06010, Malaysia
    Computer Engineering Department, University of Technology, Baghdad 10066, Iraq)

  • Sardar Gul Amen Aljabbari

    (School of Quantitative Sciences, College of Arts and Sciences, Universiti Utara Malaysia (UUM), Sintok, Kedah 06010, Malaysia
    Department of Financial and Banking, College of Business Administration and Financial Science, Al-Kitab University, Altun Kupri, Kirkuk 36015, Iraq)

  • Abbas AlZubaidi

    (Biomedical Engineering Division, University of Saskatchewan, Saskatoon, SK S7N 5C9, Canada)

  • Noraziah Haji Man

    (School of Quantitative Sciences, College of Arts and Sciences, Universiti Utara Malaysia (UUM), Sintok, Kedah 06010, Malaysia)

Abstract

This article discusses an approximate scheme for solving one-dimensional heat-like and wave-like equations in fuzzy environment based on the homotopy perturbation method (HPM). The concept of topology in homotopy is used to create a convergent series solution of the fuzzy equations. The objective of the study is to formulate the double parametric fuzzy HPM to obtain approximate solutions of fuzzy heat-like and fuzzy wave-like equations. The fuzzification and the defuzzification analysis for the double parametric form of fuzzy numbers of the fuzzy heat-like and the fuzzy wave-like equations is carried out. The proof of convergence of the solution under the developed approximate scheme is provided. The effectiveness of the proposed method is tested by numerically solving examples of fuzzy heat-like and wave-like equations where results indicate that the approach is efficient not only in terms of accuracy but also with respect to CPU time consumption.

Suggested Citation

  • Ali Fareed Jameel & Sarmad A. Jameel Altaie & Sardar Gul Amen Aljabbari & Abbas AlZubaidi & Noraziah Haji Man, 2020. "Double Parametric Fuzzy Numbers Approximate Scheme for Solving One-Dimensional Fuzzy Heat-Like and Wave-Like Equations," Mathematics, MDPI, vol. 8(10), pages 1-26, October.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:10:p:1737-:d:425832
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    Citations

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    Cited by:

    1. Mawia Osman & Yonghui Xia & Omer Abdalrhman Omer & Ahmed Hamoud, 2022. "On the Fuzzy Solution of Linear-Nonlinear Partial Differential Equations," Mathematics, MDPI, vol. 10(13), pages 1-49, June.
    2. Sunil B. Bhoi & Jayesh M. Dhodiya, 2024. "Multi-objective faculty course assignment problem based on the double parametric form of fuzzy preferences," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 34(2), pages 1-16.

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