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

Abstract

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 $$f$$ f and $$f'$$ f ? readily, instead of the evaluations of $$f$$ f only when solving the HFDE. We present a $$O(h^4)$$ O ( h 4 ) method that requires only three evaluations of $$f$$ 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.