Numerical simulation of the regularized long wave equation by He's homotopy perturbation method

2007 ◽  
Vol 369 (3) ◽  
pp. 173-179 ◽  
Author(s):  
Mustafa Inc ◽  
Yavuz Uğurlu
Keyword(s):  
Numerical Simulation ◽  
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.

scholarly journals Application of Homotopy Perturbation Method with an Auxiliary Term for Nonlinear Dropping Equations Arisen in Polymer Packaging System

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Xiang Hong ◽  
Jun Wang ◽  
Li-xin Lu
Keyword(s):  
Numerical Simulation ◽  
Perturbation Method ◽  
Analytical Solutions ◽  
Homotopy Perturbation Method ◽  
Equation Of Motion ◽  
High Accuracy ◽  
Second Order ◽  
Packaging System ◽  
Homotopy Perturbation ◽  
Approximate Analytical Solutions

The homotopy perturbation method (HPM) with an auxiliary term was applied to obtain approximate analytical solutions of polymer cushioning packaging system. The second-order solution of the equation of motion was obtained and compared with the numerical simulation solution solved by the Runge-Kutta algorithm. The results showed the high accuracy of this modified HPM with convenient calculation.

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