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

• Main Authors: Ali Fareed Jameel, Sarmad A. Jameel Altaie, Sardar Gul Amen Aljabbari, Abbas AlZubaidi, Noraziah Haji Man
• Format: Article
• Language: English
• Published: MDPI AG 2020-10-01
• Series: Mathematics
• Subjects: fuzzy partial differential equation; fuzzy heat-like equation; fuzzy wave-like equation; homotopy perturbation method (HPM); fuzzy numbers
• Online Access: https://www.mdpi.com/2227-7390/8/10/1737

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.