By using the method of successive approximation, we prove the existence and uniqueness of a solution of the fuzzy differential equation x′(t)= f(t,x(t)), x(t0)= x0. We also consider an -approximate solution of the above fuzzy differential equation.

We introduce ABC-schemes, a new class of linearly implicit one-step methods for numerical integration of stiff ordinary differential equation systems. Formulas of ABC-schemes invoke the Jacobian of differential system similary to the methods of Rosenbrock type, but unlike the latter they include also the square of the Jacobian matrix.

We firstly present a generalized concept of higher-order differentiability for fuzzy functions. Then we interpret Nth-order fuzzy differential equations using this concept. We introduce new definitions of solution to fuzzy differential equations. Some examples are provided for which both the new solutions and the former ones to the fuzzy initial value problems are presented and compared. We pre...

In this paper, solution of fuzzy differential equation under general differentiability is obtained by simulink. The simulink solution is equivalent or very close to the exact solution of the problem. Accuracy of the simulink solution to this problem is qualitatively better. An illustrative numerical example is presented for the proposed method. Keywords—Fuzzy differential equation, Generalized ...

In this paper, an improved predictor-corrector methods (IPC) to solve fuzzy differential equation under generalized differentiability are discussed. The methods proposed here are based on generalized characterization theorem. Using the Generalized Characterization we can translate a fuzzy differential equation into two ODE systems. Also, the convergence and stability of the proposed methods are...

In the recently developed Krylov deferred correction (KDC) methods for ordinary differential equation initial value problems [11], a Picard-type collocation formulation is preconditioned using low-order time integration schemes based on spectral deferred correction (SDC), and the resulting system is solved efficiently using a Newton-Krylov method. Existing analyses show that these KDC methods a...

We study conditions under which the solutions of a fuzzy integral equation are bounded. 1. Introduction. The concept of set-valued functions and their calculus [2] were found useful in some problems in economics [3], as well as in control theory [17]. Later on, the notion of H-differentiability was introduced by Puri and Ralesku in order to extend the differential of set-valued functions to tha...

The fuzzy differential and integral equations are important part of the fuzzy analysis theory and they have the important value of theory and application in control theory. Seikkala in [8] has defined the fuzzy derivative which is the generalization of the Hukuhara derivative in [7], the fuzzy integral which is the same as that of Dubois and prade [1], and by means of the extension principle of...