An efficient higher order numerica lalgorithm for solving real life application problems in an uncertain environment using triangular fuzzy numer

Many researchers have proposed numerical approaches for solving fuzzy nonlinear equations (FNE). Most of the methods used are based on the Newton algorithm. The main difficulty in solving these FNEs is obtaining and inverting the Hessian matrix. In this article, we propose the multi step second derivative free iterative method for solving FNE. The main advantage of our method is that it avoids calculating and inverting the Hessian matrix in each iteration, leading to a significant decrease in computational expenses. We solve some numerical examples and application problems related to the fraction of conversion of gases in an uncertain environment with graphical representations. We compare our results with the existing eighth order iterative method to show the efficiency of our proposed method.

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Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025).