Solving time-fractional nonlinear coupled Boussinesq-Burgers equations arise in propagation of shallow water waves using adomian decomposition method

2019 ◽  
Author(s):  
L. Meenatchi ◽  
M. Kaliyappan
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Shallow Water Waves ◽  
Burgers Equations ◽  
Adomian Decomposition

Mathematical studies of the solution of Burgers' equations by Adomian decomposition method

2019 ◽  
Vol 43 (5) ◽  
pp. 2171-2188 ◽  
Author(s):  
Dia Zeidan ◽  
Chi Kin Chau ◽  
Tzon‐Tzer Lu ◽  
Wei‐Quan Zheng
Keyword(s):  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Burgers Equations ◽  
Adomian Decomposition

scholarly journals Abundant Wave Accurate Analytical Solutions of the Fractional Nonlinear Hirota–Satsuma–Shallow Water Wave Equation

Fluids ◽  
2021 ◽  
Vol 6 (7) ◽  
pp. 235
Author(s):  
Chen Yue ◽  
Dianchen Lu ◽  
Mostafa M. A. Khater
Keyword(s):  
Wave Equation ◽  
Fractional Derivative ◽  
Shallow Water ◽  
Analytical Solutions ◽  
Water Wave ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Conformable Fractional Derivative ◽  
Adomian Decomposition ◽  
Fractional System

This research paper targets the fractional Hirota’s analytical solutions–Satsuma (HS) equations. The conformable fractional derivative is employed to convert the fractional system into a system with an integer–order. The extended simplest equation (ESE) and modified Kudryashov (MKud) methods are used to construct novel solutions of the considered model. The solutions’ accuracy is investigated by handling the computational solutions with the Adomian decomposition method. The solutions are explained in some different sketches to demonstrate more novel properties of the considered model.

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

2021 ◽  
Vol 25 (5) ◽  
pp. 623-632
Author(s):  
L. Noeiaghdam ◽  
S. Noeiaghdam ◽  
D. N. Sidorov
Keyword(s):  
Wave Equation ◽  
Shallow Water ◽  
Water Wave ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Numerical Results ◽  
Stochastic Arithmetic ◽  
Shallow Water Wave ◽  
Adomian Decomposition ◽  
Dynamical Control

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.

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