Dynamical control on the Adomian decomposition method for solving shallow water wave equation

Author:

Noeiaghdam L.1,Noeiaghdam S.2ORCID,Sidorov D. N.3ORCID

Affiliation:

1. Amirkabir University of Technology

2. Irkutsk National Research Technical University; South Ural State University

3. Irkutsk National Research Technical University; L. A. Melentiev Institute of Energy Systems of Siberian Branch of the Russian Academy of Sciences

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.

Publisher

Irkutsk National Research Technical University

Subject

General Medicine

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