Solving Nonsmooth Interval Equations with Slopes

In this paper, the problem of finding all zeros of an continuously interval function in a given interval is considered. A new method for solving this problem is proposed. It is based on the idea of isolating the endpoints of interval zeros and the technique of interval slopes. We develop the theory of the new method and apply it on a set of smooth functions and a set of nonsmooth functions respectively. In case of smooth functions, We compare the new method to a similar one from [6]. And the numerical results show the efficiency of our new method.In case of nonsmooth functions, we can gain the reliable results too. As far as know, the method we proposed is the first one which could solve the nonsmooth interval functions.