On New Solutions of Fuzzy Hybrid Differential Equations by Novel Approaches

Abstract

The goal of this paper is to find the best of two sixth-order methods, namely, RK-Huta and RK–Butcher methods for solving the fuzzy hybrid systems. We state a necessary definition and theorem in terms of consistency for convergence, and finally, we compare the obtained numerical results of two different methods with analytical solution using two different numerical examples. In addition to that, we generalize the solutions obtained by RK-6 Huta and RK-6 Butcher methods (same order different stage methods) for both the problems we handled. We are proposing these two methods in order to reduce the error in accuracy and to establish these two methods are better than any other existing numerical methods. The best of two sixth-order methods are found by the error analysis study for both the problems. Also, we show whether the change in number of stages of same order methods affects the accuracy of the approximation or not.