scholarly journals Solution of Free-Particle Radial Dependant Schrödinger Equation Using He's Homotopy Perturbation Method

2010 ◽  
Vol 4 (8) ◽  
Author(s):  
A. A. Mahasneh ◽  
A. M. Al-Qararah
Keyword(s):  
Schrödinger Equation ◽  
Perturbation Method ◽  
Schrodinger Equation ◽  
Homotopy Perturbation Method ◽  
Free Particle ◽  
Homotopy Perturbation

Homotopy Perturbation Method for Solving Nonlinear Differential- Difference Equations

2010 ◽  
Vol 65 (6-7) ◽  
pp. 511-517 ◽  
Author(s):  
Mohamed M. Mousa ◽  
Aidarkhan Kaltayev
Keyword(s):  
Schrödinger Equation ◽  
Perturbation Method ◽  
Exact Solutions ◽  
Difference Equations ◽  
Analytical Solutions ◽  
Schrodinger Equation ◽  
Homotopy Perturbation Method ◽  
Nonlinear Schrodinger Equation ◽  
Lattice Equation ◽  
Homotopy Perturbation

In this paper, the homotopy perturbation method (HPM) is extended to obtain analytical solutions for some nonlinear differential-difference equations (NDDEs). The discretized modified Kortewegde Vries (mKdV) lattice equation and the discretized nonlinear Schrodinger equation are taken as examples to illustrate the validity and the great potential of the HPM in solving such NDDEs. Comparisons between the results of the presented method and exact solutions are made. The results reveal that the HPM is very effective and convenient for solving such kind of equations.

scholarly journals An Approximate Analytical Solution of the Nonlinear Schrödinger Equation with Harmonic Oscillator Using Homotopy Perturbation Method and Laplace-Adomian Decomposition Method

2018 ◽  
Vol 2018 ◽  
pp. 1-11
Author(s):  
Emad K. Jaradat ◽  
Omar Alomari ◽  
Mohammad Abudayah ◽  
Ala’a M. Al-Faqih
Keyword(s):  
Schrödinger Equation ◽  
Harmonic Oscillator ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Homotopy Perturbation Method ◽  
Adomian Decomposition Method ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Homotopy Perturbation ◽  
Adomian Decomposition

The Laplace-Adomian Decomposition Method (LADM) and Homotopy Perturbation Method (HPM) are both utilized in this research in order to obtain an approximate analytical solution to the nonlinear Schrödinger equation with harmonic oscillator. Accordingly, nonlinear Schrödinger equation in both one and two dimensions is provided to illustrate the effects of harmonic oscillator on the behavior of the wave function. The available literature does not provide an exact solution to the problem presented in this paper. Nevertheless, approximate analytical solutions are provided in this paper using LADM and HPM methods, in addition to comparing and analyzing both solutions.

On Spectral-Homotopy Perturbation Method Solution of Nonlinear Differential Equations in Bounded Domains

2013 ◽  
Vol 1 (1) ◽  
pp. 25-37
Author(s):  
Ahmed A. Khidir
Keyword(s):  
Perturbation Method ◽  
Homotopy Perturbation Method ◽  
Nonlinear Boundary ◽  
Nonlinear Differential Equations ◽  
Iteration Algorithm ◽  
Test Problems ◽  
Nonlinear Boundary Value Problems ◽  
Homotopy Perturbation ◽  
Spectral Technique ◽  
Homotopy Analysis

In this study, a combination of the hybrid Chebyshev spectral technique and the homotopy perturbation method is used to construct an iteration algorithm for solving nonlinear boundary value problems. Test problems are solved in order to demonstrate the efficiency, accuracy and reliability of the new technique and comparisons are made between the obtained results and exact solutions. The results demonstrate that the new spectral homotopy perturbation method is more efficient and converges faster than the standard homotopy analysis method. The methodology presented in the work is useful for solving the BVPs consisting of more than one differential equation in bounded domains. 

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