Exact solutions for nonlinear Burgers' equation by homotopy perturbation method

2009 ◽  
Vol 25 (4) ◽  
pp. 833-842 ◽  
Author(s):  
J. Biazar ◽  
H. Ghazvini
Keyword(s):  
Perturbation Method ◽  
Exact Solutions ◽  
Homotopy Perturbation Method ◽  
Burgers Equation ◽  
Homotopy Perturbation

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.

The Homotopy-Perturbation Method for Solving Klein-Gordon-Type Equations with Unbounded Right- Hand Side

2009 ◽  
Vol 64 (1-2) ◽  
pp. 149-152 ◽  
Author(s):  
Afgan Aslanov
Keyword(s):  
Perturbation Method ◽  
Exact Solutions ◽  
Homotopy Perturbation Method ◽  
Initial Conditions ◽  
Homotopy Perturbation ◽  
Right Hand ◽  
Klein Gordon ◽  
New Type ◽  
Solvable Problems

The approximate and/or exact solutions of the generalized Klein-Gordon- and sine-Gordon-type equations are obtained. We introduce a new type of initial conditions to extend the class of solvable problems

scholarly journals The Application of the Homotopy Perturbation Method and the Homotopy Analysis Method to the Generalized Zakharov Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Hassan A. Zedan ◽  
Eman El Adrous
Keyword(s):  
Perturbation Method ◽  
Exact Solutions ◽  
Homotopy Analysis Method ◽  
Homotopy Perturbation Method ◽  
Initial Conditions ◽  
Nonlinear Problems ◽  
Analysis Method ◽  
Homotopy Perturbation ◽  
Homotopy Analysis ◽  
The Absolute

We introduce two powerful methods to solve the generalized Zakharov equations; one is the homotopy perturbation method and the other is the homotopy analysis method. The homotopy perturbation method is proposed for solving the generalized Zakharov equations. The initial approximations can be freely chosen with possible unknown constants which can be determined by imposing the boundary and initial conditions; the homotopy analysis method is applied to solve the generalized Zakharov equations. HAM is a strong and easy-to-use analytic tool for nonlinear problems. Computation of the absolute errors between the exact solutions of the GZE equations and the approximate solutions, comparison of the HPM results with those of Adomian’s decomposition method and the HAM results, and computation the absolute errors between the exact solutions of the GZE equations with the HPM solutions and HAM solutions are presented.

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