scholarly journals Solitonic Solutions for Homogeneous KdV Systems by Homotopy Analysis Method

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Mohammed Ali ◽  
Marwan Alquran ◽  
Mahmoud Mohammad
Keyword(s):  
Homotopy Analysis Method ◽  
Stability Region ◽  
Analysis Method ◽  
Auxiliary Parameter ◽  
Analytical Treatment ◽  
Third Order ◽  
Kdv Equations ◽  
Two Component ◽  
Homotopy Analysis ◽  
The Stability

We study two-component evolutionary systems of a homogeneous KdV equations of second and third order. The homotopy analysis method (HAM) is used for analytical treatment of these systems. The auxiliary parameterhof HAM is freely chosen from the stability region of theh-curve obtained for each proposed system.

scholarly journals Constructing analytic solutions on the Tricomi equation

Open Physics ◽  
2018 ◽  
Vol 16 (1) ◽  
pp. 143-148 ◽  
Author(s):  
Emran Khoshrouye Ghiasi ◽  
Reza Saleh
Keyword(s):  
Homotopy Analysis Method ◽  
Series Solution ◽  
Variational Iteration Method ◽  
Approximate Solutions ◽  
Analytic Solutions ◽  
Analysis Method ◽  
Auxiliary Parameter ◽  
Tricomi Equation ◽  
Homotopy Analysis ◽  
Optimal Values

AbstractIn this paper, homotopy analysis method (HAM) and variational iteration method (VIM) are utilized to derive the approximate solutions of the Tricomi equation. Afterwards, the HAM is optimized to accelerate the convergence of the series solution by minimizing its square residual error at any order of the approximation. It is found that effect of the optimal values of auxiliary parameter on the convergence of the series solution is not negligible. Furthermore, the present results are found to agree well with those obtained through a closed-form equation available in the literature. To conclude, it is seen that the two are effective to achieve the solution of the partial differential equations.

Homotopy Analysis Method

2017 ◽  
pp. 173-226
Keyword(s):  
Homotopy Analysis Method ◽  
Series Solution ◽  
Nonlinear Partial Differential Equations ◽  
Analytic Method ◽  
Series Solutions ◽  
Analysis Method ◽  
Auxiliary Parameter ◽  
Convergence Region ◽  
Homotopy Analysis ◽  
And Control

In this chapter, the analytic solution of nonlinear partial differential equations arising in heat transfer is obtained using the newly developed analytic method, namely the Homotopy Analysis Method (HAM). The homotopy analysis method provides us with a new way to obtain series solutions of such problems. This method contains the auxiliary parameter provides us with a simple way to adjust and control the convergence region of series solution. By suitable choice of the auxiliary parameter, we can obtain reasonable solutions for large modulus.

Homotopy Analysis Method for a Class of Holling II's Model

2013 ◽  
Vol 694-697 ◽  
pp. 2891-2894
Author(s):  
Xiu Rong Chen
Keyword(s):  
Homotopy Analysis Method ◽  
Analysis Method ◽  
Auxiliary Parameter ◽  
Convergence Region ◽  
Solution Series ◽  
Homotopy Analysis ◽  
And Control

In this paper, the homotopy analysis method (HAM) is used for solving a class of Holling IIs model. The approximation solutions were obtained by HAM, and contain the auxiliary parameter h which provides us with a convenient way to adjust and control convergence region and rate of solution series. This results showed that this method is valid and feasible to the model.

scholarly journals Series Solution of the System of Fuzzy Differential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
M. S. Hashemi ◽  
J. Malekinagad ◽  
H. R. Marasi
Keyword(s):  
Differential Equations ◽  
Homotopy Analysis Method ◽  
Series Solution ◽  
Analysis Method ◽  
Auxiliary Parameter ◽  
Convergence Region ◽  
Solution Series ◽  
Homotopy Analysis ◽  
Contour Plots ◽  
And Control

The homotopy analysis method (HAM) is proposed to obtain a semianalytical solution of the system of fuzzy differential equations (SFDE). The HAM contains the auxiliary parameterħ, which provides us with a simple way to adjust and control the convergence region of solution series. Concept ofħ-meshes and contour plots firstly are introduced in this paper which are the generations of traditionalh-curves. Convergency of this method for the SFDE has been considered and some examples are given to illustrate the efficiency and power of HAM.

Homotopy Analysis Method for a Prey-Predator System with Holling IV Functional Response

2014 ◽  
Vol 687-691 ◽  
pp. 1286-1291 ◽  
Author(s):  
Jia Shang Yu ◽  
Jia Ju Yu
Keyword(s):  
Functional Response ◽  
Homotopy Analysis Method ◽  
Analysis Method ◽  
Auxiliary Parameter ◽  
Convergence Region ◽  
Solution Series ◽  
Homotopy Analysis ◽  
And Control ◽  
Predator System

In this paper, the homotopy analysis method is used for solving a prey-predator system with holling IV functional response. The approximation solutions were obtained by homotopy analysis method, and contain the auxiliary parameter h which provides us with a convenient way to adjust and control convergence region and rate of solution series. This result showed that this method is valid and feasible for the system.

Stability Analysis of a Prey-Predator Model by Using Homotopy Analysis Method

2012 ◽  
Vol 166-169 ◽  
pp. 2855-2858
Author(s):  
Hong Yan Cao
Keyword(s):  
Nonlinear Dynamics ◽  
Equilibrium Point ◽  
Homotopy Analysis Method ◽  
Zero Point ◽  
Positive Equilibrium ◽  
Analysis Method ◽  
Homotopy Analysis ◽  
Predator Model ◽  
Positive Equilibrium Point ◽  
The Stability

A prey-predator model was considered. Using the methods of the modern nonlinear dynamics and homotopy analysis method (HAM), its stability was discussed. Firstly, we found the system’s positive equilibrium point and shifted it to zero point through transformation. Secondly, we analyzed the stability of the system at the equilibrium point. Lastly, we analyzed the transformed system by HAM. We support our analytical findings with numerical simulation.

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