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Fatoorehchi H.,University of Tehran | Rach R.,The George Adomian Center for Applied Mathematics | Abolghasemi H.,University of Tehran
Romanian Journal of Physics | Year: 2015

We develop a family of improved iterative formulas for computation of matrix inverses. Towards this purpose, we first consider a general class of scalar Newtontype root-finders, which have been improved by incorporating the Adomian decomposition method. Subsequently, we extend such scalar root-finders to their respective matrix analogs by means of an innovative computer screening program. Our formulas are shown, through numerical experiments, to surpass five well-known iterative schemes taken from the literature, both in terms of the CPU elapsed time and iteration count. According to these results, one of our new formulas saves more than 13% in CPU time in the worst case, when compared with all five previous iterative methods. In addition, the convergence order of a simple member of the family of our matrix inversion formulas was proven to be at least three to better elucidate our new approach. © 2015, Editura Academiei Romane. All rights reserved. Source


Fatoorehchi H.,University of Tehran | Fatoorehchi H.,Iran Liquefied Natural Gas Co. | Rach R.,The George Adomian Center for Applied Mathematics | Tavakoli O.,University of Tehran | Abolghasemi H.,University of Tehran
Chemical Engineering Communications | Year: 2015

In this study, an efficient iterative algorithm is devised to handle a nonlinear equation arising in estimation of thermodynamic properties at supercritical conditions. The approach is based on a synergistic combination of the classic Newton-Raphshon algorithm and the Adomian decomposition method. We demonstrate that the proposed method enjoys a higher degree of accuracy while requiring fewer iterations to reach a specific solution compared to that by the Newton-Raphson algorithm. To illustrate the efficiency of the aforementioned solution technique, several numerical examples are provided. The proposed method has been easily implemented in computer codes to provide parametric, not just numeric, solutions to the model equations. Consequently, one can derive other thermodynamic properties, which have not been treated parametrically to date, based on our new combined approach. © 2015, Copyright Taylor & Francis Group, LLC. Source


Fatoorehchi H.,University of Tehran | Abolghasemi H.,University of Tehran | Zarghami R.,University of Tehran | Rach R.,The George Adomian Center for Applied Mathematics | von Freeden S.,University of Stuttgart
Korean Journal of Chemical Engineering | Year: 2015

An efficient method based on the Faddeev-Leverrier algorithm combined with the Adomian decomposition method is devised to facilitate the stability analysis of multi-input multi-output control systems. In contrast to prior eigenvalue algorithms, our method affords all eigenvalues of the state matrix, either real or complex. Specifically, the calculation of the complex eigenvalues is made possible through special canonical forms, mainly involving square root operators, of the characteristic equation of the state matrix. Moreover, the proposed method does not require an initial guess, which is often a matter of concern since an inappropriate guess can cause failure in such available schemes. For the sake of illustration, a number of numerical examples, including chemical reaction processes, are also provided that demonstrate the efficiency of our new technique. © 2015, Korean Institute of Chemical Engineers, Seoul, Korea. Source


Fatoorehchi H.,University of Tehran | Abolghasemi H.,University of Tehran | Zarghami R.,University of Tehran | Rach R.,The George Adomian Center for Applied Mathematics
Canadian Journal of Chemical Engineering | Year: 2015

A number of control schemes including nonlinear feedback, dislocated feedback, and speed feedback have been proposed and assessed for a bromate-malonic acid-cerium Belousov-Zhabotinsky batch reaction process. The tuning parameters of the Oregonator model were firstly adjusted based on a UV-vis spectrophotometric analysis in the experimental part of the research. The adjusted Oregonator model successfully reproduced the innate induction time and periodicity of the BZ-batch system. Subsequently, the controllers were implemented and numerical simulations were carried out by employing the multi-stage Adomian decomposition method. The nominal analysis method was used to study the linear stability of each design. All the controlled systems were found to be linearly stable for certain continuous regions of controller gain. The performance of the proposed control laws was assessed and the dislocated feedback control strategy was shown to be able to drive the system states toward desired setpoints quickly. Furthermore, the validity of the dislocated feedback control design was doubly ensured by the sliding mode control theory. It was found that those feedback schemes which manipulate cerium ion concentration can be practically realized by means of electrochemical oxidation or oxygen aeration. Our results were confirmed by the Simulink software package and the block diagram representations are included in the paper. © 2015 Canadian Society for Chemical Engineering. Source


Fatoorehchi H.,University of Tehran | Abolghasemi H.,University of Tehran | Rach R.,The George Adomian Center for Applied Mathematics
Journal of Petroleum Science and Engineering | Year: 2014

The use of the Hankinson-Thomas-Phillips correlation for prediction of the natural gas compressibility factor is a common practice in natural gas engineering calculations. However, this equation suffers a serious deficiency from a computational viewpoint; in that it is not explicit with respect to the z-factor and hence is subject to time-consuming trial and error procedures. In this paper, we propose an explicit series expansion equivalent to the Hankinson-Thomas-Phillips equation by the aid of a powerful mathematical technique known as the Adomian decomposition method. Furthermore, we have enhanced our formula by a applying nonlinear convergence accelerator algorithm, namely the Shanks transform. The proposed equation is simple, easy to use, and is shown to be extremely accurate in reproducing the experimental PVT data of natural gases. Moreover, in contrast to the previous numerical algorithms such as the Newton-Raphson algorithm, the explicit nature of our formula obviates the need for any initial guess as an input for calculation of the z-factor. Such independence permits our formula to always quickly converge to the correct z-factor. © 2014 Elsevier B.V. Source

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