Premium
Trajectory optimization techniques in chemical reaction engineering: I. Boundary condition iteration methods
Author(s) -
Jaspan R. K.,
Coull J.
Publication year - 1971
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.690170124
Subject(s) - convergence (economics) , generalization , boundary (topology) , boundary value problem , mathematics , variable (mathematics) , function (biology) , trajectory , state variable , state (computer science) , mathematical optimization , computer science , algorithm , mathematical analysis , physics , astronomy , evolutionary biology , economics , biology , economic growth , thermodynamics
A new generalization of boundary condition iteration (BCI) methods is developed, based on a suggestion of Denn and Aris. This simplifies to Horn's equation for up to two state equations and to previous boundary iteration methods when\documentclass{article}\pagestyle{empty}\begin{document}$$ \partial H/\partial \vec u = \vec 0 $$\end{document}is explicitly soluble for\documentclass{article}\pagestyle{empty}\begin{document}$$ \vec u_{opt} $$\end{document}as a function of the constants, the state and the adjoint variables. The new general method is also applicable when this latter function is unobtainable. Distinct improvement in the convergence rates of the existing BCI methods has been obtained through the introduction of a correction specific to each state variable. A convergence procedure for use with Horn's equation is proposed and the resultant algorithm has desirable properties.