Soft Comput DOI 10.1007/s00500-014-1314-9 METHODOLOGIES AND APPLICATION

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 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