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In this paper, we propose an iterative spectral method for solving differential equations with initial values on large intervals. In the proposed method, we first extend the Legendre wavelet suitable for large intervals, and then the Legendre-Guass collocation points of the Legendre wavelet are derived. Using this strategy, the iterative spectral method converts the differential equation to a set of algebraic equations. Solving these algebraic equations yields an approximate solution for the differential equation. The proposed method is illustrated by some numerical examples, and the result is compared with the exponentially fitted Runge-Kutta method. Our proposed method is simple and highly accurate.

In this note we show that the example presented in a recent paper by Ghazanfari et al. is incorrect. Namely, the "exact solution" suggested by the authors is not solution of the given fuzzy differential equation (FDE). Indeed, the authors have proposed an exact solution which is independent from the initial condition. So, we obtain the correct exact solution using the characterization theorem proposed by Bede et al. under Seikkala differentiability. Also, some details are given for the mentioned example.

In this paper, we firstly introduce system of first order fuzzy differential equations. Then, we convert the problem to two crisp systems of first order differential equations. For numerical aspects, we apply exponentially fitted Runge Kutta method to solve the fuzzy problems. We solve some well-known examples in order to demonstrate the applicability and accuracy of results.

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