scholarly journals Optimal Homotopy Asymptotic Method to Nonlinear Damped Generalized Regularized Long-Wave Equation

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
R. Nawaz ◽  
S. Islam ◽  
I. A. Shah ◽  
M. Idrees ◽  
H. Ullah
Keyword(s):  
Wave Equation ◽  
Approximate Solution ◽  
Asymptotic Method ◽  
Iteration Method ◽  
Variational Iteration Method ◽  
Numerical Examples ◽  
Long Wave ◽  
Regularized Long Wave Equation ◽  
Optimal Homotopy Asymptotic Method ◽  
2D Images

A new semianalytical technique optimal homology asymptotic method (OHAM) is introduced for deriving approximate solution of the homogeneous and nonhomogeneous nonlinear Damped Generalized Regularized Long-Wave (DGRLW) equation. We tested numerical examples designed to confine the features of the proposed scheme. We drew 3D and 2D images of the DGRLW equations and the results are compared with that of variational iteration method (VIM). Results reveal that OHAM is operative and very easy to use.

scholarly journals An Extension of the Optimal Homotopy Asymptotic Method to Coupled Schrödinger-KdV Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Hakeem Ullah ◽  
Saeed Islam ◽  
Muhammad Idrees ◽  
Mehreen Fiza ◽  
Zahoor Ul Haq
Keyword(s):  
Approximate Solution ◽  
Perturbation Method ◽  
Asymptotic Method ◽  
Iteration Method ◽  
Homotopy Perturbation Method ◽  
Kdv Equation ◽  
Variational Iteration Method ◽  
Variational Iteration ◽  
Homotopy Perturbation ◽  
Optimal Homotopy Asymptotic Method

We consider the approximate solution of the coupled Schrödinger-KdV equation by using the extended optimal homotopy asymptotic method (OHAM). We obtained the extended OHAM solution of the problem and compared with the exact, variational iteration method (VIM) and homotopy perturbation method (HPM) solutions. The obtained solution shows that extended OHAM is effective, simpler, easier, and explicit and gives a suitable way to control the convergence of the approximate solution.

scholarly journals A Good Numerical Method for the Solution of Generalized Regularized Long Wave Equation

2017 ◽  
Vol 11 (6) ◽  
pp. 72 ◽  
Author(s):  
Fuchang Zheng ◽  
Shuhong Bao ◽  
Yulan Wang ◽  
Shuguang Li ◽  
Zhiyuan Li
Keyword(s):  
Wave Equation ◽  
Numerical Method ◽  
High Precision ◽  
Science And Technology ◽  
Convergence Speed ◽  
Fast Convergence ◽  
Numerical Examples ◽  
Long Wave ◽  
Regularized Long Wave Equation

The generalized regularized long wave equation is very important that can be applied in the field of physics,science and technology. Some authors have put forward many different numerical method, but the precision isnot enough high. In this paper, we will illustrate the high-precision numerical method to solve the generalizedregularized long wave equation. Three numerical examples are studied to demonstrate the accuracy of thepresent method. Results obtained by our method indicate new algorithm has the following advantages: smallcomputational work, fast convergence speed and high precision.

scholarly journals Approximate Solution of Two-Dimensional Nonlinear Wave Equation by Optimal Homotopy Asymptotic Method

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
H. Ullah ◽  
S. Islam ◽  
L. C. C. Dennis ◽  
T. N. Abdelhameed ◽  
I. Khan ◽  
...  
Keyword(s):  
Wave Equation ◽  
Approximate Solution ◽  
Nonlinear Wave ◽  
Nonlinear Wave Equation ◽  
Asymptotic Method ◽  
Series Solution ◽  
Wave Equations ◽  
Nonlinear Wave Equations ◽  
Two Dimensional ◽  
Optimal Homotopy Asymptotic Method

The two-dimensional nonlinear wave equations are considered. Solution to the problem is approximated by using optimal homotopy asymptotic method (OHAM). The residual and convergence of the proposed method to nonlinear wave equation are presented through graphs. The resultant analytic series solution of the two-dimensional nonlinear wave equation shows the effectiveness of the proposed method. The comparison of results has been made with the existing results available in the literature.

Euler operators and conservation laws of the BBM equation

1979 ◽  
Vol 85 (1) ◽  
pp. 143-160 ◽  
Author(s):  
Peter J. Olver
Keyword(s):  
Wave Equation ◽  
Conservation Laws ◽  
Calculus Of Variations ◽  
Long Wave ◽  
Regularized Long Wave Equation ◽  
Formal Calculus ◽  
Euler Operators ◽  
Bbm Equation

AbstractThe BBM or Regularized Long Wave Equation is shown to possess only three non-trivial independent conservation laws. In order to prove this result, a new theory of Euler-type operators in the formal calculus of variations will be developed in detail.

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