A Comparison Between Adomian’s Decomposition Method and the Homotopy Perturbation Method for Solving Nonlinear Differential Equations

2012 ◽  
Vol 12 (8) ◽  
pp. 793-797 ◽  
Author(s):  
E. Babolian ◽  
A.R. Vahidi ◽  
Z. Azimzadeh
Keyword(s):  
Differential Equations ◽  
Perturbation Method ◽  
Decomposition Method ◽  
Homotopy Perturbation Method ◽  
Nonlinear Differential Equations ◽  
Homotopy Perturbation ◽  
Adomian’S Decomposition Method

scholarly journals Homotopy Perturbation Method

2017 ◽  
pp. 24-61
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Perturbation Method ◽  
Exact Solutions ◽  
Homotopy Perturbation Method ◽  
Numerical Solutions ◽  
Nonlinear Differential Equations ◽  
Homotopy Perturbation ◽  
Wide Range ◽  
Transfer Problems

The homotopy perturbation method (HPM) is employed to compute an approximation to the solution of the system of nonlinear differential equations governing on the problem. It has been attempted to show the capabilities and wide-range applications of the homotopy perturbation method in comparison with the previous ones in solving heat transfer problems. The obtained solutions, in comparison with the exact solutions admit a remarkable accuracy. A clear conclusion can be drawn from the numerical results that the HPM provides highly accurate numerical solutions for nonlinear differential equations.

Analysis of Fractional Nonlinear Differential Equations Using the Homotopy Perturbation Method

2011 ◽  
Vol 66 (1-2) ◽  
pp. 87-92 ◽  
Author(s):  
Mehmet Ali Balcı ◽  
Ahmet Yıldırım
Keyword(s):  
Differential Equations ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Nonlinear Differential Equations ◽  
Time Derivative ◽  
Numerical Results ◽  
Homotopy Perturbation ◽  
Fractional Time Derivative

In this study, we used the homotopy perturbation method (HPM) for solving fractional nonlinear differential equations. Three models with fractional-time derivative of order α, 0<α <1, are considered and solved. The numerical results demonstrate that this method is relatively accurate and easily implemented.

Application of Homotopy Perturbation Method with Chebyshev Polynomials to Nonlinear Problems

2010 ◽  
Vol 65 (1-2) ◽  
pp. 65-70
Author(s):  
Changbum Chun
Keyword(s):  
Differential Equations ◽  
Perturbation Method ◽  
Chebyshev Polynomials ◽  
Homotopy Perturbation Method ◽  
Nonlinear Differential Equations ◽  
Nonlinear Problems ◽  
Homotopy Perturbation ◽  
He’S Polynomials ◽  
Efficiency And Reliability

AbstractIn this paper, we present an efficient modification of the homotopy perturbation method by using Chebyshev’s polynomials and He’s polynomials to solve some nonlinear differential equations. Some illustrative examples are given to demonstrate the efficiency and reliability of the modified homotopy perturbation method.

scholarly journals Rational Biparameter Homotopy Perturbation Method and Laplace-Padé Coupled Version

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
Hector Vazquez-Leal ◽  
Arturo Sarmiento-Reyes ◽  
Yasir Khan ◽  
Uriel Filobello-Nino ◽  
Alejandro Diaz-Sanchez
Keyword(s):  
Power Series ◽  
Differential Equations ◽  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Nonlinear Differential Equations ◽  
Approximate Solutions ◽  
Van Der Pol Oscillator ◽  
Van Der Pol ◽  
Homotopy Perturbation ◽  
Physical Phenomena

The fact that most of the physical phenomena are modelled by nonlinear differential equations underlines the importance of having reliable methods for solving them. This work presents the rational biparameter homotopy perturbation method (RBHPM) as a novel tool with the potential to find approximate solutions for nonlinear differential equations. The method generates the solutions in the form of a quotient of two power series of different homotopy parameters. Besides, in order to improve accuracy, we propose the Laplace-Padé rational biparameter homotopy perturbation method (LPRBHPM), when the solution is expressed as the quotient of two truncated power series. The usage of the method is illustrated with two case studies. On one side, a Ricatti nonlinear differential equation is solved and a comparison with the homotopy perturbation method (HPM) is presented. On the other side, a nonforced Van der Pol Oscillator is analysed and we compare results obtained with RBHPM, LPRBHPM, and HPM in order to conclude that the LPRBHPM and RBHPM methods generate the most accurate approximated solutions.

Sign in / Sign up

Export Citation Format

Share Document