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In this paper, the solution of fuzzy differential equations is approximated numerically using diagonally implicit multistep block method of order four. The multistep block method is well known as an efficient and accurate method for solving ordinary differential equations, hence in this paper the method will be used to solve the fuzzy initial value problems where the initial value is a symmetric triangular fuzzy interval. The triangular fuzzy number is not necessarily symmetric, however by imposing symmetry the definition of a triangular fuzzy number can be simplified. The symmetric triangular fuzzy interval is a triangular fuzzy interval that has same left and right width of membership function from the center. Due to this, the parametric form of symmetric triangular fuzzy number is simple and the performing arithmetic operations become easier. In order to interpret the fuzzy problems, Seikkala's derivative approach is implemented. Characterization theorem is then used to translate the problems into a system of ordinary differential equations. The convergence of the introduced method is also proved. Numerical examples are given to investigate the performance of the proposed method. It is clearly shown in the results that the proposed method is comparable and reliable in solving fuzzy differential equations. [ABSTRACT FROM AUTHOR]

In this paper a fuzzy Improved Runge-Kutta method for solving first-order fuzzy differential equations is proposed. The scheme is two step in nature and is based on the Improved Runge-kutta method for solving ordinary differential equations. Here, the fourth order method with three stages is explained. In this method some new parameter be exploited to increase the accuracy in comparison with other same stage existing methods. The convergence of the method is proven, and several numerical examples are experienced to illustrate the effectiveness of the method. [ABSTRACT FROM AUTHOR]

In this paper, a fuzzy general linear method of order three for solving fuzzy Volterra integro-differential equations of second kind is proposed. The general linear method is operated using the both internal stages of Runge-Kutta method and multivalues of a multisteps method. The derivation of general linear method is based on the theory of B-series and rooted trees. Here, the fuzzy general linear method using the approach of generalized Hukuhara differentiability and combination of composite Simpson's rules together with Lagrange interpolation polynomial is constructed for numerical solution of fuzzy volterra integro-differential equations. To illustrate the performance of the method, the numerical results are compared with some existing numerical methods. [ABSTRACT FROM AUTHOR]

Abstract: 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. [Copyright &y& Elsevier]