Creating and handling box valued functions used in numerical methods

The paper presents new results on box valued functions (so-called zone functions) introduced by the author. The first part gives a general description of the methods of zone functions (with respect to some classes of nonlinear problems), a new theorem on zone function rules and figures that help (simplify) creating zone functions. The second part gives a new algorithm which is appropriate for handling zone functions by advanced programming languages. A computer program in C++ and some numerical examples are also presented.