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

IF 1 4区 物理与天体物理 Q3 PHYSICS, MATHEMATICAL
Hamzeh Zureigat, Mohammad A. Tashtoush, Ali F. Al Jassar, Emad A. Az-Zo’bi, Mohammad W. Alomari
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引用次数: 1

Abstract

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.
用改进的Crank-Nicolson方法解复Dirichlet条件下的复模糊热方程
复模糊集(CFSs)最近成为一种有效的工具,用于扩展模糊集的范围,使其在复平面的单位圆盘内包含更广泛的范围。本文在文献中首次探讨了复模糊数,并介绍了复模糊数在复模糊偏微分方程中的应用,该方程涉及复模糊热方程的Hukuhara可微性。研究人员利用隐式有限差分格式,即Crank-Nicolson方法,来处理复杂的模糊热方程。该问题的模糊性来自于振幅项和相位项的系数,以及初始条件和边界条件,并将凸归一化三角模糊数扩展到复平面上的单元盘。研究人员在提出的数值方法中利用了CFS理论的特性和优点,从而为CFS理论下的稳定性提供了新的证明。数值算例验证了该方法的可靠性和可行性,结果与精确解和相关理论观点吻合较好。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Advances in Mathematical Physics
Advances in Mathematical Physics 数学-应用数学
CiteScore
2.40
自引率
8.30%
发文量
151
审稿时长
>12 weeks
期刊介绍: Advances in Mathematical Physics publishes papers that seek to understand mathematical basis of physical phenomena, and solve problems in physics via mathematical approaches. The journal welcomes submissions from mathematical physicists, theoretical physicists, and mathematicians alike. As well as original research, Advances in Mathematical Physics also publishes focused review articles that examine the state of the art, identify emerging trends, and suggest future directions for developing fields.
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