Numerical solutions of fuzzy differential equations by an efficient Runge-Kutta method with generalized differentiability

In this paper, an extended fourth-order Runge-Kutta method is studied to approximate the solutions of first-order fuzzy differential equations using a generalized characterization theorem. In this method, new parameters are utilized in order to enhance the order of accuracy of the solutions using evaluations of both f and f′, instead of using the evaluations of f only. The proposed extended Runge-Kutta method and its error analysis, which guarantees pointwise convergence, are given in detail. Furthermore, the accuracy and efficiency of the proposed method are demonstrated in a series of numerical experiments.