Numerical solution of Korteweg–de Vries-Burgers equation by the modified variational iteration algorithm-II arising in shallow water waves

2020 ◽  
Vol 95 (4) ◽  
pp. 045210 ◽  
Author(s):  
Hijaz Ahmad ◽  
Aly R Seadawy ◽  
Tufail A Khan
Keyword(s):  
Numerical Solution ◽  
Shallow Water ◽  
Water Waves ◽  
Burgers Equation ◽  
Iteration Algorithm ◽  
Shallow Water Waves ◽  
Variational Iteration ◽  
De Vries

scholarly journals Two Reliable Methods for The Solution of Fractional Coupled Burgers’ Equation Arising as a Model of Polydispersive Sedimentation

2019 ◽  
Vol 4 (2) ◽  
pp. 523-534 ◽  
Author(s):  
Ali Kurt ◽  
Mehmet Şenol ◽  
Orkun Tasbozan ◽  
Mehar Chand
Keyword(s):  
Water Waves ◽  
Fractional Derivatives ◽  
Burgers Equation ◽  
Approximate Solutions ◽  
Iteration Algorithm ◽  
Shallow Water Waves ◽  
Fractional Differential ◽  
Reliable Methods ◽  
Coupled Burgers Equation ◽  
Partial Fractional Differential Equations

AbstractIn this article, we attain new analytical solution sets for nonlinear time-fractional coupled Burgers’ equations which arise in polydispersive sedimentation in shallow water waves using exp-function method. Then we apply a semi-analytical method namely perturbation-iteration algorithm (PIA) to obtain some approximate solutions. These results are compared with obtained exact solutions by tables and surface plots. The fractional derivatives are evaluated in the conformable sense. The findings reveal that both methods are very effective and dependable for solving partial fractional differential equations.

scholarly journals Computational Analysis of Shallow Water Waves with Korteweg-de Vries Equation

2017 ◽  
Vol 0 (0) ◽  
pp. 0-0 ◽  
Author(s):  
Turgut Ak ◽  
Houria Triki ◽  
Sharanjeet Dhawan ◽  
Samir Kumar Bhowmik ◽  
Seithuti Philemon Moshokoa ◽  
...  
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Computational Analysis ◽  
Vries Equation ◽  
Shallow Water Waves ◽  
De Vries

scholarly journals Coupling Conditions for Water Waves at Forks

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 434 ◽  
Author(s):  
Jean-Guy Caputo ◽  
Denys Dutykh ◽  
Bernard Gleyse
Keyword(s):  
Conservation Laws ◽  
Numerical Solution ◽  
Shallow Water ◽  
Water Waves ◽  
Large Amplitude ◽  
Narrow Channel ◽  
Effective Model ◽  
Interface Conditions ◽  
Shallow Water Waves ◽  
Coupling Conditions

We considered the propagation of nonlinear shallow water waves in a narrow channel presenting a fork. We aimed at computing the coupling conditions for a 1D effective model, using 2D simulations and an analysis based on the conservation laws. For small amplitudes, this analysis justifies the well-known Stoker interface conditions, so that the coupling does not depend on the angle of the fork. We also find this in the numerical solution. Large amplitude solutions in a symmetric fork also tend to follow Stoker’s relations, due to the symmetry constraint. For non symmetric forks, 2D effects dominate so that it is necessary to understand the flow inside the fork. However, even then, conservation laws give some insight in the dynamics.

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