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 to encompass wider ranges within unit disk in complex plane. This study explores numbers and introduces their application first time literature address partial differential equation that involves heat under Hukuhara differentiability. The researchers utilize an implicit finite difference scheme, namely Crank–Nicolson method, tackle equations. problem’s fuzziness arises from coefficients both amplitude phase terms, well initial boundary conditions, with Convex normalized triangular extended take advantage properties benefits CFS theory proposed numerical methods subsequently provide new proof stability theory. A example is presented demonstrate approach’s reliability feasibility, results showing good agreement exact solution relevant theoretical aspects.