Legendre Operational Differential Matrix for Solving Fuzzy Differential Equations with Trapezoidal Fuzzy Function Coefficients

In this work, we used the Legendre operational differential matrix method based on Tau method to obtain the fuzzy approximate-analytical solutions of the fuzzy differential equations in which the coefficients are trapezoidal fuzzy function. This method allows for the fuzzy solution of the fuzzy initial ( or boundary) value problems to be computed in the form of an infinite fuzzy series .Also, this method enables to approximate the fuzzy exact-analytical solutions with high efficiency, as these solutions can be resorted to if it is not possible to find the exact solutions of these fuzzy problems. We introduced a comparison between the approximate solutions that we computed and the exact solutions of the chosen problem, as we found the absolute error. According to the numerical results, the series solutions that we found are accurate solutions and very close to the exact solutions.