A Valid Dynamical Control on the Reverse Osmosis System Using the CESTAC Method

The aim of this study is to present a novel method to find the optimal solution of the reverse osmosis (RO) system. We apply the Sinc integration rule with single exponential (SE) and double exponential (DE) decays to find the approximate solution of the RO. Moreover, we introduce the stochastic ari...

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Bibliographic Details
Published in:Mathematics (Basel) 2021-01, Vol.9 (1), p.48
Main Authors: Noeiaghdam, Samad, Sidorov, Denis, Zamyshlyaeva, Alyona, Tynda, Aleksandr, Dreglea, Aliona
Format: Article
Language:English
Subjects:
Approximation
CADNA library
CESTAC method
Control algorithms
double exponential decay
Errors
Floating point arithmetic
Food science
Integral equations
Iterative methods
Libraries
Numerical analysis
Regularization methods
Reverse osmosis
reverse osmosis system
sinc integration rule
single exponential decay
Theorems
Water treatment
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Summary:The aim of this study is to present a novel method to find the optimal solution of the reverse osmosis (RO) system. We apply the Sinc integration rule with single exponential (SE) and double exponential (DE) decays to find the approximate solution of the RO. Moreover, we introduce the stochastic arithmetic (SA), the CESTAC method (Controle et Estimation Stochastique des Arrondis de Calculs) and the CADNA (Control of Accuracy and Debugging for Numerical Applications) library instead of the mathematical methods based on the floating point arithmetic (FPA). Applying this technique, we would be able to find the optimal approximation, the optimal error and the optimal iteration of the method. The main theorems are proved to support the method analytically. Based on these theorems, we can apply a new stopping condition in the numerical procedure instead of the traditional absolute error. These theorems show that the number of common significant digits (NCSDs) of exact and approximate solutions are almost equal to the NCSDs of two successive approximations. The numerical results are obtained for both SE and DE Sinc integration rules based on the FPA and the SA. Moreover, the number of iterations for various ε are computed in the FPA. Clearly, the DE case is more accurate and faster than the SE for finding the optimal approximation, the optimal error and the optimal iteration of the RO system.
ISSN:2227-7390
2227-7390
DOI:10.3390/math9010048