A Runge-Kutta method with reduced number of function evaluations to solve hybrid fuzzy differential equations

In this paper, we employ a numerical algorithm to solve first-order hybrid fuzzy differential equation (HFDE) based on the high order Runge–Kutta method. It is assumed that the user will evaluate both f and f ′ readily, instead of the evaluations of f only when solving the HFDE. We present a O(h4) method that requires only three evaluations of f . Moreover, we consider the characterization theorem of Bede to solve the HFDE numerically. The convergence of the method will be proven and numerical examples are shown with a comparison to the conventional solutions.