Open AccessDynamical control on the Adomian decomposition method for solving shallow water wave equation
Author(s) -
L. Noeiaghdam,
Samad Noeiaghdam,
Denis Sidorov
Publication year - 2021
Publication title -
vestnik irkutskogo gosudarstvennogo tehničeskogo universiteta
Language(s) - English
Resource type - Journals
eISSN - 2500-1590
pISSN - 1814-3520
DOI - 10.21285/1814-3520-2021-5-623-632
Subject(s) - adomian decomposition method , debugging , decomposition , decomposition method (queueing theory) , computer science , mathematics , nonlinear system , scheme (mathematics) , mathematical optimization , partial differential equation , mathematical analysis , ecology , physics , discrete mathematics , quantum mechanics , biology , programming language
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.