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

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...

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Bibliographic Details
Published in:Mathematics (Basel) 2020-10, Vol.8 (10), p.1737
Main Authors: Jameel, Ali Fareed, Altaie, Sarmad A. Jameel, Aljabbari, Sardar Gul Amen, AlZubaidi, Abbas, Man, Noraziah Haji
Format: Article
Language:English
Subjects:
Computational mathematics
Convergence
fuzzy heat-like equation
Fuzzy logic
fuzzy numbers
fuzzy partial differential equation
Fuzzy sets
fuzzy wave-like equation
homotopy perturbation method (HPM)
Partial differential equations
Perturbation methods
Topology
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Summary: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math8101737