REVERSE ITERATION IN CHEMICAL PROCESS SIMULATION

A new technique for generating approximations of Julia sets, called re verse iteration, is proposed. The concept of reverse iteration is simp le and based on the idea of solving an iterative map of the general fo rm Z(k) = G(Z(k-1), p) for Z(k-1) instead of Z(k). It is shown that if the process of reverse iteration is initiated at any singular point, the collection of inverse images must be members of the Julia set sinc e singular points are in the Julia set and the Julia set is closed, Th is sequence of reverse iterates, say {Z(k-1)}, is necessarily distribu ted throughout the basin boundaries. It is also shown that reverse ite ration can have multiple inverse images and a tree structure for the J ulia see but; that the associated potential combinatorial computationa l demand is easily resolved by exploiting the fractal nature of any Ju lia set. From this, practical ways generating initial values that conv erge to solutions to the given model equations are proposed. Several e xamples and geometric illustrations are used to elucidate key concepts .