Exact solutions for non-linear Schrödinger equations by He's homotopy perturbation method

2007 ◽  
Vol 366 (1-2) ◽  
pp. 79-84 ◽  
Author(s):  
J. Biazar ◽  
H. Ghazvini
Keyword(s):  
Perturbation Method ◽  
Exact Solutions ◽  
Homotopy Perturbation Method ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Homotopy Perturbation ◽  
Non Linear

Application of the Homotopy Perturbation Method to Linear and Nonlinear Schrödinger Equations

2008 ◽  
Vol 63 (3-4) ◽  
pp. 140-144 ◽  
Author(s):  
Mohamed M. Mousaa ◽  
Shahwar F. Ragab
Keyword(s):  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Nonlinear Schrödinger Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Analytic Treatment ◽  
Nonlinear Schrödinger ◽  
Homotopy Perturbation ◽  
Nonlinear Schrodinger Equations ◽  
Linear And Nonlinear

He’s homotopy perturbation method (HPM) is applied to linear and nonlinear Schrödinger equations for obtaining exact solutions. The HPM is used for an analytic treatment of these equations. The results reveal that the HPM is very effective, convenient and quite accurate to such types of partial differential equations.

scholarly journals Homotopy perturbation method for viscous heating in plane Couette flow

2013 ◽  
Vol 17 (5) ◽  
pp. 1355-1360 ◽  
Author(s):  
Yin-Shan Yun ◽  
Chaolu Temuer
Keyword(s):  
Perturbation Method ◽  
Exact Solutions ◽  
Couette Flow ◽  
Taylor Series ◽  
Homotopy Perturbation Method ◽  
Viscous Heating ◽  
Plane Couette Flow ◽  
Homotopy Perturbation ◽  
Non Linear

In this paper, the problem of viscous heating in plane Couette flow is considered by the homotopy perturbation method. The non-linear terms are expanded to Taylor series of the homotopy parameter. The obtained solutions are shown graphically and are compared with the exact solutions. The obtained results illustrate the efficiency and convenience of the 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.

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