Dynamical control on the Adomian decomposition method for solving shallow water wave equation
https://doi.org/10.21285/1814-3520-2021-5-623-632
Abstract
The aim of this study is to apply a novel technique to control the accuracy and error of the Adomian decomposition method (ADM) for solving nonlinear shallow water wave equation. The ADM is among semi-analytical and powerful methods for solving many mathematical and engineering problems. We apply the Controle et Estimation Stochastique des Arrondis de Calculs (CESTAC) method which is based on stochastic arithmetic (SA). Also instead of applying mathematical packages we use the Control of Accuracy and Debugging for Numerical Applications (CADNA) library. In this library we will write all codes using C++ programming codes. Applying the method we can find the optimal numerical results, error and step of the ADM and they are the main novelties of this research. The numerical results show the accuracy and efficiency of the novel scheme.
About the Authors
L. Noeiaghdam
Amirkabir University of Technology
Islamic Republic of Iran
Islamic Republic of Iran
Laleh Noeiaghdam, Postgraduate Student, Department of Civil and Environmental Engineering
350, Hafez Ave, Valiasr Square, Tehran, 1591634311
S. Noeiaghdam
Irkutsk National Research Technical University; South Ural State University
Russian Federation
Russian Federation
Samad Noeiaghdam, Senior Lecturer, Industrial Mathematics Laboratory, Baikal School of BRICS, Irkutsk National Research Technical University; Senior Researcher of the Department of Applied Mathematics and Programming, South Ural State University
83 Lermontov St., Irkutsk 664074
76, Lenin pr., Chelyabinsk 454080
D. N. Sidorov
Irkutsk National Research Technical University; L. A. Melentiev Institute of Energy Systems of Siberian Branch of the Russian Academy of Sciences
Russian Federation
Russian Federation
Denis N. Sidorov, Dr. Sci. (Physics & Mathematics), Professor of RAS, Head of the Laboratory of Industrial Mathematics, Baikal School of BRICS, Irkutsk National Research Technical University; Chief Researcher of the Department of Applied Mathematics, L. A. Melentiev Institute of Energy Systems of Siberian Branch of the Russian Academy of Sciences,
83 Lermontov St., Irkutsk 664074
130, Lermontov St., Irkutsk 664033
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Review
For citations:
Noeiaghdam L., Noeiaghdam S., Sidorov D.N. Dynamical control on the Adomian decomposition method for solving shallow water wave equation. iPolytech Journal. 2021;25(5):623-632. https://doi.org/10.21285/1814-3520-2021-5-623-632
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