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

Ali Fareed Jameel, Sarmad A. Jameel Altaie, Sardar Gul Amen Aljabbari, Abbas AlZubaidi and Noraziah Haji Man
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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
Sardar Gul Amen Aljabbari: School of Quantitative Sciences, College of Arts and Sciences, Universiti Utara Malaysia (UUM), Sintok, Kedah 06010, Malaysia
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

Mathematics, 2020, vol. 8, issue 10, 1-26

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.

Keywords: fuzzy partial differential equation; fuzzy heat-like equation; fuzzy wave-like equation; homotopy perturbation method (HPM); fuzzy numbers (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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