In this paper, we employed fuzzy transforms to present a new method for solving the problem through a second-order fuzzy initial value. The advantage of the fuzzy transform method is that, unlike other methods (e.g. high-order fuzzy Taylor series), it does not require any higher-order derivative calculation, thus reducing the computational cost. In two examples, the results of the newly proposed method were examined against several conventional methods, indicating the more desirable performance of the new method.
