Application of the homotopy perturbation method to the modified regularized long-wave equation

2009 ◽  
Vol 26 (2) ◽  
pp. 399-411 ◽  
Author(s):  
Talha Achouri ◽  
Khaled Omrani
Keyword(s):  
Wave Equation ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Homotopy Perturbation ◽  
Long Wave ◽  
Regularized Long Wave Equation

scholarly journals Approximate Analytical Solutions of the Regularized Long Wave Equation Using the Optimal Homotopy Perturbation Method

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Constantin Bota ◽  
Bogdan Căruntu
Keyword(s):  
Perturbation Method ◽  
Analytical Solutions ◽  
Homotopy Perturbation Method ◽  
Nonlinear Partial Differential Equations ◽  
Accelerated Convergence ◽  
Homotopy Perturbation ◽  
Long Wave ◽  
Approximate Analytical Solutions ◽  
Regularized Long Wave Equation ◽  
Regular Homotopy

The paper presents the optimal homotopy perturbation method, which is a new method to find approximate analytical solutions for nonlinear partial differential equations. Based on the well-known homotopy perturbation method, the optimal homotopy perturbation method presents an accelerated convergence compared to the regular homotopy perturbation method. The applications presented emphasize the high accuracy of the method by means of a comparison with previous results.

Homotopy Perturbation Method for Time-Fractional Shock Wave Equation

2011 ◽  
Vol 3 (6) ◽  
pp. 774-783 ◽  
Author(s):  
Mithilesh Singh ◽  
Praveen Kumar Gupta
Keyword(s):  
Shock Wave ◽  
Wave Equation ◽  
Perturbation Method ◽  
Numerical Solution ◽  
Fractional Derivatives ◽  
Homotopy Perturbation Method ◽  
Initial Conditions ◽  
Numerical Results ◽  
Homotopy Perturbation

AbstractA scheme is developed to study numerical solution of the time-fractional shock wave equation and wave equation under initial conditions by the homotopy perturbation method (HPM). The fractional derivatives are taken in the Caputo sense. The solutions are given in the form of series with easily computable terms. Numerical results are illustrated through the graph.

scholarly journals An Approached Solution of Wave Equation with Cubic Damping by Homotopy Perturbation Method (HPM), Regular Pertubation Method (RPM) and Adomian Decomposition Method (ADM)

2018 ◽  
Vol 10 (2) ◽  
pp. 166
Author(s):  
Moussa BAGAYOGO ◽  
Youssouf PARE ◽  
Youssouf MINOUNGOU
Keyword(s):  
Wave Equation ◽  
Perturbation Method ◽  
Decomposition Method ◽  
Homotopy Perturbation Method ◽  
Initial Conditions ◽  
Adomian Decomposition Method ◽  
Homotopy Perturbation ◽  
Adomian Decomposition ◽  
The Given

In this study, we consider the wave equation with cubic damping with its initial conditions. Homotopy Perturbation Method (HPM), Regular Pertubation Method (RPM) and Adomian decomposition Method (ADM) are applied to this equation. Then, the solution yielding the given initial conditions is gained. Finally, the solutions obtained by each method are compared.

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