Dynamical control of accuracy in the fuzzy Runge-Kutta methods to estimate the solution of a fuzzy differential equation

In this paper, a reliable scheme is proposed to solve fuzzy differential equations by fuzzy Runge-Kutta method of order $m$. For this purpose, the stochastic arithmetic and CESTAC method are applied to validate the results. In order to implement the C++ codes, the CADNA library is used. In this case, the optimal step size is found. The examples illustrate the efficiency and importance of using the stochastic arithmetic in place of the floating-point arithmetic.