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

Samad Noeiaghdam, Denis Sidorov, Alyona Zamyshlyaeva, Aleksandr Tynda and Aliona Dreglea
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Samad Noeiaghdam: Industrial Mathematics Laboratory, Baikal School of BRICS, Irkutsk National Research Technical University, 664074 Irkutsk, Russia
Denis Sidorov: Industrial Mathematics Laboratory, Baikal School of BRICS, Irkutsk National Research Technical University, 664074 Irkutsk, Russia
Alyona Zamyshlyaeva: Department of Applied Mathematics and Programming, South Ural State University, Lenin Prospect 76, 454080 Chelyabinsk, Russia
Aleksandr Tynda: Higher and Applied Mathematics Department, Penza State University, 440026 Penza, Russia
Aliona Dreglea: Industrial Mathematics Laboratory, Baikal School of BRICS, Irkutsk National Research Technical University, 664074 Irkutsk, Russia

Mathematics, 2020, vol. 9, issue 1, 1-17

Abstract: 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.

Keywords: sinc integration rule; double exponential decay; single exponential decay; CESTAC method; CADNA library; reverse osmosis system (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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