Abstract: This paper presents a computational framework for solving fuzzy partial differential equations (FPDEs) using the α-cut approach coupled with finite difference schemes. The fuzzy heat equation is employed as a model problem, where the fuzziness in initial or boundary conditions is addressed using α-level decomposition. The resulting interval-valued PDEs are discretized using the explicit forward-time central-space (FTCS) method. The reconstruction of fuzzy solutions from multiple α-level simulations provides an envelope or "fuzzy band" that quantifies the impact of uncertainty in the model parameters. Numerical examples demonstrate the efficacy of the proposed method and illustrate the propagation of uncertainty in space and time.

Keywords: Fuzzy PDE, α-cut method, Finite difference scheme, Heat equation, Interval analysis, Uncertainty modeling, Fuzzy band.

Downloads: | DOI: 10.17148/IARJSET.2023.101021