Performance analysis of an iterative method for solving nonlinear motion of an object in an uncertain environment using triangular fuzzy number

Purpose In this work, we focus on developing a second-derivative-free iterative method for solving fuzzy nonlinear equations arising in various application problems, such as the motion of an object vertically and horizontally. One of the main difficulties in solving fuzzy nonlinear equations is computing the second-order derivative. Design/methodology/approach In this work, we proposed a second-derivative-free fifth-order method. Consequently, there is no longer a need to calculate and invert the Jacobian matrix during each iteration, significantly reducing computational cost. Findings The proposed approach effectively addresses nonlinear equations when fuzzy numbers are involved, with enhanced flexibility and accuracy. We discuss some application-based numerical examples to demonstrate the efficacy of the proposed method and compare it with the existing Newton method, modified Newton method, and second-derivative-free fifth-order iterative method. The comparison of results indicates that the present technique is superior to existing ones. Finally, we have discussed some case studies of the motion of an object in vertical and downward directions. Research limitations/implications In this study, our work is limited to triangular fuzzy numbers. Originality/value In this paper, we developed a new second-derivative-free higher-order iterative method for solving fuzzy nonlinear equations. We discussed some numerical examples to check the validity of our proposed method.