Autonomous block method for uncertainty analysis in first-order real-world models using fuzzy initial value problem

This article employs fuzzy derivatives and fuzzy differential equations (FDEs) to handle uncertainty in real-world applications. When exact answers are unavailable, numerical approaches are utilized to derive approximations for FDE. The autonomous two-step block method (TBM) with two higher fuzzy derivatives is used to discover optimum solutions to first-order FDEs with greater absolute accuracy. The technique competency is evaluated by analyzing first-order real-world models with fuzzy initial value problems (FIVPs). Using fuzzy calculus principles, we establish a novel universal fuzzification formulation of the TBM approach with the Taylor series. TBM is a convergent, zero-stable, and absolute stability region approach for solving linear and nonlinear fuzzy models, with a focus on regulating the convergence of approximate solutions. The developed method offers approximations for difficulties encountered in real life and is a transformational and workable method for solving first-order FIVPs.