Two algorithms for approximate construction of the set of positional absorption in the game problem of pursuit

Consideration is given to the differential game on the finite period of time in which the first player has to guarantee that the phase point will entry the terminal set and the second one must ensure the evasion of the terminal set on this interval. Is proposed a method for approximate construction of the set of positional absorption, i.e, the set of all initial points for which the problem of pursuit posed for the first player is solvable. The method is based on unification constructions and structures close to them. Relations defining the system of sets that approximates the set of positional absorption are written out. The convergence of the approximating system to the set of positional absorption is proved.