Fuzzy Numerical Solution via Finite Difference Scheme of Wave Equation in Double Parametrical Fuzzy Number Form

Maryam Almutairi, Hamzeh Zureigat, Ahmad Izani Ismail and Ali Fareed Jameel
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Maryam Almutairi: Department of Mathematics, Shaqra University, Shaqra 11921, Saudi Arabia
Hamzeh Zureigat: Departments of Mathematics, Faculty of Science and Technology, Jadara University, Irbid 21110, Jordan
Ahmad Izani Ismail: School of Mathematical Sciences, Universiti Sains Malaysia, Pulau Pinang 11800, Malaysia
Ali Fareed Jameel: School of Quantitative Sciences, College of Arts and Sciences, Universiti Utara Malaysia (UUM), Sintok 06010, Malaysia

Mathematics, 2021, vol. 9, issue 6, 1-16

Abstract: The use of fuzzy partial differential equations has become an important tool in which uncertainty or vagueness exists to model real-life problems. In this article, two numerical techniques based on finite difference schemes that are the centered time center space and implicit schemes to solve fuzzy wave equations were used. The core of the article is to formulate a new form of centered time center space and implicit schemes to obtain numerical solutions fuzzy wave equations in the double parametric fuzzy number approach. Convex normalized triangular fuzzy numbers are represented by fuzziness, based on a double parametric fuzzy number form. The properties of fuzzy set theory are used for the fuzzy analysis and formulation of the proposed numerical schemes followed by the new proof stability thermos under in the double parametric form of fuzzy numbers approach. The consistency and the convergence of the proposed scheme are discussed. Two test examples are carried out to illustrate the feasibility of the numerical schemes and the new results are displayed in the forms of tables and figures where the results show that the schemes have not only been effective for accuracy but also for reducing computational cost.

Keywords: finite difference schemes; double parametric form of fuzzy number; fuzzy partial differential equations; fuzzy wave equation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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