An improved form of optimal homotopy asymptotic method for the solution of a system of nonlinear coupled differential equations occurring in the phenomenon of fluid mechanics

2019 ◽  
Author(s):  
Liaqat Ali ◽  
Saeed Islam ◽  
Taza Gul
Keyword(s):  
Differential Equations ◽  
Fluid Mechanics ◽  
Asymptotic Method ◽  
Coupled Differential Equations ◽  
Optimal Homotopy Asymptotic Method

scholarly journals Extension of Optimal Homotopy Asymptotic Method with Use of Daftardar–Jeffery Polynomials to Coupled Nonlinear-Korteweg-De-Vries System

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-6 ◽  
Author(s):  
Rashid Nawaz ◽  
Zawar Hussain ◽  
Abraiz Khattak ◽  
Adam Khan
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Asymptotic Method ◽  
Nonlinear Partial Differential Equations ◽  
Coupled System ◽  
Higher Order ◽  
Partial Differential ◽  
De Vries ◽  
Optimal Homotopy Asymptotic Method

In this paper, Daftardar–Jeffery Polynomials are introduced in the Optimal Homotopy Asymptotic Method for solution of a coupled system of nonlinear partial differential equations. The coupled nonlinear KdV system is taken as test example. The results obtained by the proposed method are compared with the multistage Optimal Homotopy Asymptotic Method. The results show the efficiency and consistency of the proposed method over the Optimal Homotopy Asymptotic Method. In addition, accuracy of the proposed method can be improved by taking higher order approximations.

scholarly journals SOLUSI PENDEKATAN PERSAMAAN GELOMBANG FRAKSIONAL NON LINEAR MENGGUNAKAN NEW VERSION OF OPTIMAL HOMOTOPY ASYMPTOTIC METHOD

2020 ◽  
Vol 14 (4) ◽  
pp. 523-534
Author(s):  
Faiqul Fikri ◽  
Eddy Djauhari ◽  
Endang Rusyaman
Keyword(s):  
Wave Equation ◽  
Differential Equations ◽  
Asymptotic Method ◽  
Wave Equations ◽  
Percentage Error ◽  
Approximation Solution ◽  
Fractional Wave Equation ◽  
Non Linear ◽  
Fractional Wave Equations ◽  
Optimal Homotopy Asymptotic Method

Non-linear differential equations with fractional derivative order are mathematical models that are widely used in modeling physical phenomena, one of the applications of these models is non-linear fractional wave equations. Many methods for solving non-linear fractional partial differential equations, one of which is the New Version of Optimal Homotopy Asymptotic Method which is developed by Liaqat Ali in 2016. The author will use this method to solve non-linear fractional wave equations predetermined, so that the convergence of function of the approximation solution non-linear fractional wave equation can be observed and it can be observed that the function of approximation solution of non-linear fractional wave equation solution using the New Version of Optimal Homotopy Asymptotic Method is simple and has a value error using Mean Absolute Percentage Error which is categorized very well

scholarly journals Solution of Burgers’ equation appears in fluid mechanics by multistage optimal homotopy asymptotic method

2021 ◽  
pp. 343-343
Author(s):  
Fuzhang Wang ◽  
Niaz Shah ◽  
Imtiaz Ahmad ◽  
Hijaz Ahmad ◽  
Kamran Alam ◽  
...  
Keyword(s):  
Fluid Mechanics ◽  
Asymptotic Method ◽  
Large Time ◽  
Burgers Equation ◽  
Nonlinear Partial Differential Equations ◽  
Nonlinear Problems ◽  
Variational Iteration Method ◽  
Numerical Comparison ◽  
Modern Physics ◽  
Optimal Homotopy Asymptotic Method

In this article, we approximate analytical solution of Burgers? equations using the Multistage homotopy asymptotic method which are utilized in modern physics and fluid mechanics. The suggested algorithm is an accurate and simple to-utilize semi-analytic tool for nonlinear problems. In the current research we investigation the efficiency and accuracy of the method for the solution of nonlinear partial differential equations for large time span. Numerical comparison with the variational iteration method shows the efficacy and accuracy of the proposed method.

scholarly journals Optimal Homotopy Asymptotic Method for Solving Delay Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
N. Ratib Anakira ◽  
A. K. Alomari ◽  
I. Hashim
Keyword(s):  
Differential Equations ◽  
Asymptotic Method ◽  
Delay Differential Equations ◽  
Perturbation Methods ◽  
Analytic Solution ◽  
Approximate Analytic Solution ◽  
Initial Value ◽  
Optimal Homotopy Asymptotic Method ◽  
Delay Differential ◽  
First Time

We extend for the first time the applicability of the optimal homotopy asymptotic method (OHAM) to find the algorithm of approximate analytic solution of delay differential equations (DDEs). The analytical solutions for various examples of linear and nonlinear and system of initial value problems of DDEs are obtained successfully by this method. However, this approach does not depend on small or large parameters in comparison to other perturbation methods. This method provides us with a convenient way to control the convergence of approximation series. The results which are obtained revealed that the proposed method is explicit, effective, and easy to use.

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