A new fuzzy approximation method to Cauchy problems by fuzzy transform

We present new numeric methods based on the first and second degree F-transform for solving the Cauchy problem. We show that they outperform the second order Runge–Kutta method especially when a right-hand function is oscillating and/or a solution is requested on a long interval. Moreover, a new numeric method to solve fuzzy initial value problem using the F-transform is presented. The suitability of the presented new methods is theoretically justified and illustrated on various examples.