we are concerned with the development of a k−step method for the numerical solution of fuzzy initial value problems. convergence and stability of the method are also proved in detail. moreover, a specific method of order 4 is found. the numerical results show that the proposed fourth order method is efficient for solving fuzzy differential equations.

How complex could the solution be to an initial value problem given by a polynomial-time computable function? This question can be given a natural and precise sense in computational complexity theory. In this note, we put together several results stating that more conditions on the problem make the solution simpler. In particular, Lipschitz continuity alone may leave the solution polynomial-spa...

where the initial time, t0, is a given real number, the initial position, ~ ξ0 ∈ IR, is a given vector and ~ F : IR × IR → IR is a given function. We shall assume throughout these notes that ~ F is C. By definition, a solution to the initial value problem (1) on the interval I (which may be open, closed or half–open, but which, of course, contains t0) is a differentiable function ~x(t) which obeys

where the initial time, t0, is a given real number, the initial position, ~ ξ0 ∈ IR, is a given vector and ~ F : IR × IR → IR is a given function. We shall assume throughout these notes that ~ F is C. By definition, a solution to the initial value problem (1) on the interval I (which may be open, closed or half–open, but which, of course, contains t0) is a differentiable function ~x(t) which obeys