ISSN:
0001-1541
Keywords:
Chemistry
;
Chemical Engineering
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Chemistry and Pharmacology
,
Process Engineering, Biotechnology, Nutrition Technology
Notes:
Techniques are developed for using the structural information contained in algebraic equation sets to aid in the study of convergence properties of iterative equation loops.The concept of inverse mapping is applied directly in order to study convergence properties of sequences. For problems in which there exist both a direct and inverse path for the computation of iterative loops, direct substitution techniques will converge via one path and diverge via the other path. When an inverse path existed, the direct substitution method was superior to simultaneous solution techniques for the problems studied. Not all iterative loops have an inverse path. For problems in which inverse paths do not originally exist, rearrangement of the equations of an iterative loop can result in a modified loop for which an inverse path does exist. The digraph representation of an iterative loop aids in deciding whether rearrangements are feasible for a particular problem. When inverse paths cannot conveniently be obtained, direct substitution cannot be successfully used and simultaneous solution techniques such as quasi-linearization are recommended.
Additional Material:
13 Ill.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/aic.690190323
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