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Invariant imbedding, iterative linearization, and multistage countercurrent processes
Author(s) -
Lee E. Stanley
Publication year - 1970
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.690160428
Subject(s) - mathematics , linearization , countercurrent exchange , estimator , iterative method , boundary value problem , invariant (physics) , nonlinear system , mathematical analysis , control theory (sociology) , mathematical optimization , computer science , statistics , control (management) , physics , quantum mechanics , mathematical physics , thermodynamics , artificial intelligence
The equations for multistage countercurrent operations are difference equations of the boundary‐value type, which are generally solved by trial and error or iterative procedures. The invariant imbedding concept is used to solve these boundary‐value problems as initial‐value problems. It is shown that by the combined use of invariant imbedding and iterative linearization, a sequence of estimator equations for the missing terminal conditions is obtained. These estimator equations can be used to obtain the desired terminal conditions and the number of stages required to perform a specified separation.