A Solution of the Complex Fuzzy Heat Equation in Terms of Complex Dirichlet Conditions Using a Modified Crank–Nicolson Method

Complex fuzzy sets (CFSs) have recently emerged as a potent tool for expanding the scope of fuzzy sets to encompass wider ranges within the unit disk in the complex plane. This study explores complex fuzzy numbers and introduces their application for the first time in the literature to address a com...

Full description

Saved in:
Bibliographic Details
Published in:Advances in mathematical physics 2023-09, Vol.2023, p.1-8
Main Authors: Zureigat, Hamzeh, Tashtoush, Mohammad A., Jassar, Ali F. Al, Az-Zo’bi, Emad A., Alomari, Mohammad W.
Format: Article
Language:English
Subjects:
Accuracy
Approximation
Boundary conditions
Brain
Crank-Nicholson method
Dirichlet problem
Exact solutions
Finite difference method
Fuzzy sets
Mathematical models
Numbers
Numerical methods
Partial differential equations
Semantics
Thermodynamics
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:Complex fuzzy sets (CFSs) have recently emerged as a potent tool for expanding the scope of fuzzy sets to encompass wider ranges within the unit disk in the complex plane. This study explores complex fuzzy numbers and introduces their application for the first time in the literature to address a complex fuzzy partial differential equation that involves a complex fuzzy heat equation under Hukuhara differentiability. The researchers utilize an implicit finite difference scheme, namely the Crank–Nicolson method, to tackle complex fuzzy heat equations. The problem’s fuzziness arises from the coefficients in both amplitude and phase terms, as well as in the initial and boundary conditions, with the Convex normalized triangular fuzzy numbers extended to the unit disk in the complex plane. The researchers take advantage of the properties and benefits of CFS theory in the proposed numerical methods and subsequently provide a new proof of the stability under CFS theory. A numerical example is presented to demonstrate the proposed approach’s reliability and feasibility, with the results showing good agreement with the exact solution and relevant theoretical aspects.
ISSN:1687-9120
1687-9139
DOI:10.1155/2023/6505227