Analytical solutions of linear and nonlinear Klein-Fock-Gordon equation

2015 ◽  
Vol 4 (1) ◽  
Author(s):  
Najeeb Alam Khan ◽  
Sajida Rasheed
Keyword(s):  
Analytical Solutions ◽  
Gordon Equation ◽  
Series Solutions ◽  
Analysis Method ◽  
Auxiliary Parameter ◽  
Convergence Region ◽  
Relativistic Version ◽  
Approximate Analytical Solutions ◽  
Homotopy Analysis ◽  
Linear And Nonlinear

AbstractIn this paper, we deal with some linear and nonlinear Klein-Fock-Gordon (KFG) equations, which is a relativistic version of the Schrödinger equation. The approximate analytical solutions are obtained by using the homotopy analysis method (HAM). The efficiency of the HAM is that it provides a practical way to control the convergence region of series solutions by introducing an auxiliary parameter }. Analytical results presented are in agreement with the existing results in open literature, which confirm the effectiveness of this method.

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.

scholarly journals Direct Solution ofnth-Order IVPs by Homotopy Analysis Method

2009 ◽  
Vol 2009 ◽  
pp. 1-15 ◽  
Author(s):  
A. Sami Bataineh ◽  
M. S. M. Noorani ◽  
I. Hashim
Keyword(s):  
Homotopy Analysis Method ◽  
Direct Solution ◽  
Analysis Method ◽  
Auxiliary Parameter ◽  
Initial Value ◽  
Convergence Region ◽  
Runge Kutta Method ◽  
Approximate Analytical Solutions ◽  
Homotopy Analysis ◽  
Comparable Accuracy

Direct solution of a class ofnth-order initial value problems (IVPs) is considered based on the homotopy analysis method (HAM). The HAM solutions contain an auxiliary parameter which provides a convenient way of controlling the convergence region of the series solutions. The HAM gives approximate analytical solutions which are of comparable accuracy to the seven- and eight-order Runge-Kutta method (RK78).

Analytic Solution of the Sharma-Tasso-Olver Equation by Homotopy Analysis Method

2010 ◽  
Vol 65 (4) ◽  
pp. 285-290 ◽  
Author(s):  
Saeid Abbasbandy ◽  
Mahnaz Ashtiani ◽  
Esmail Babolian
Keyword(s):  
Homotopy Analysis Method ◽  
Analytic Solution ◽  
Series Solutions ◽  
Analysis Method ◽  
Auxiliary Parameter ◽  
Convergence Region ◽  
Homotopy Analysis ◽  
Convergence Control ◽  
And Control ◽  
Convergence Control Parameter

An analytic technique, the homotopy analysis method (HAM), is applied to obtain the kink solution of the Sharma-Tasso-Olver equation. The homotopy analysis method is one of the analytic methods and provides us with a new way to obtain series solutions of such problems. HAM contains the auxiliary parameter ħwhich gives us a simple way to adjust and control the convergence region of series solution. “Due to this reason, it seems reasonable to rename ħthe convergence-control parameter” [1].

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.

scholarly journals Approximate Analytical Solutions to Conformable Modified Burgers Equation Using Homotopy Analysis Method

2019 ◽  
Vol 33 (1) ◽  
pp. 159-167 ◽  
Author(s):  
Ali Kurt ◽  
Orkun Tasbozan
Keyword(s):  
Analytical Solution ◽  
Analytical Solutions ◽  
Homotopy Analysis Method ◽  
Burgers Equation ◽  
Approximate Analytical Solution ◽  
Analysis Method ◽  
Conformable Derivative ◽  
Modified Burgers Equation ◽  
Approximate Analytical Solutions ◽  
Homotopy Analysis

AbstractIn this paper the authors aspire to obtain the approximate analytical solution of Modified Burgers Equation with newly defined conformable derivative by employing homotopy analysis method (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.

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