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An analytical study for (2 + 1)-dimensional Schrödinger equation.

Ghanbari B - ScientificWorldJournal (2014)

Bottom Line: The validity of this method has successfully been accomplished by applying it to find the solution of some of its variety forms.The results obtained by homotopy analysis method have been compared with those of exact solutions.The results show that the solution of homotopy analysis method is in a good agreement with the exact solution.

View Article: PubMed Central - PubMed

Affiliation: Department of Basic Sciences, Kermanshah University of Technology, Kermanshah, Iran.

ABSTRACT
In this paper, the homotopy analysis method has been applied to solve (2 + 1)-dimensional Schrödinger equations. The validity of this method has successfully been accomplished by applying it to find the solution of some of its variety forms. The results obtained by homotopy analysis method have been compared with those of exact solutions. The main objective is to propose alternative methods of finding a solution, which do not require small parameters and avoid linearization and physically unrealistic assumptions. The results show that the solution of homotopy analysis method is in a good agreement with the exact solution.

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The ℏ-curves for the 7th-order of HAM approximation of u(0,0, 0.5, h) for Example 2; dotted line: real part of approximation; solid line: imaginary part of approximation.
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fig2: The ℏ-curves for the 7th-order of HAM approximation of u(0,0, 0.5, h) for Example 2; dotted line: real part of approximation; solid line: imaginary part of approximation.

Mentions: Again, the value ℏ = −1 was chosen based on the ℏ-curve shown in Figure 2. Then the series solution expression is obtained by HAM as(24)u(x,y,t)=icosh⁡⁡(x)cosh⁡⁡(y) ×(1−it−12!t2+i3!t3+14!t4+⋯),which coincides with the exact solutions (22).


An analytical study for (2 + 1)-dimensional Schrödinger equation.

Ghanbari B - ScientificWorldJournal (2014)

The ℏ-curves for the 7th-order of HAM approximation of u(0,0, 0.5, h) for Example 2; dotted line: real part of approximation; solid line: imaginary part of approximation.
© Copyright Policy - open-access
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC3927856&req=5

fig2: The ℏ-curves for the 7th-order of HAM approximation of u(0,0, 0.5, h) for Example 2; dotted line: real part of approximation; solid line: imaginary part of approximation.
Mentions: Again, the value ℏ = −1 was chosen based on the ℏ-curve shown in Figure 2. Then the series solution expression is obtained by HAM as(24)u(x,y,t)=icosh⁡⁡(x)cosh⁡⁡(y) ×(1−it−12!t2+i3!t3+14!t4+⋯),which coincides with the exact solutions (22).

Bottom Line: The validity of this method has successfully been accomplished by applying it to find the solution of some of its variety forms.The results obtained by homotopy analysis method have been compared with those of exact solutions.The results show that the solution of homotopy analysis method is in a good agreement with the exact solution.

View Article: PubMed Central - PubMed

Affiliation: Department of Basic Sciences, Kermanshah University of Technology, Kermanshah, Iran.

ABSTRACT
In this paper, the homotopy analysis method has been applied to solve (2 + 1)-dimensional Schrödinger equations. The validity of this method has successfully been accomplished by applying it to find the solution of some of its variety forms. The results obtained by homotopy analysis method have been compared with those of exact solutions. The main objective is to propose alternative methods of finding a solution, which do not require small parameters and avoid linearization and physically unrealistic assumptions. The results show that the solution of homotopy analysis method is in a good agreement with the exact solution.

Show MeSH
Related in: MedlinePlus