Explicit series solutions of some linear and nonlinear Schrodinger equations via the homotopy analysis method

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37 Citations (Scopus)

Abstract

In this paper, by means of the homotopy analysis method (HAM), the solutions of some Schrodinger equations are exactly obtained in the form of convergent Taylor series. The HAM contains the auxiliary parameter ℏ, that provides a convenient way of controlling the convergent region of series solutions. This analytical method is employed to solve linear and nonlinear examples to obtain the exact solutions. HAM is a powerful and easy-to-use analytic tool for nonlinear problems.

Original languageEnglish
Pages (from-to)1196-1207
Number of pages12
JournalCommunications in Nonlinear Science and Numerical Simulation
Volume14
Issue number4
DOIs
Publication statusPublished - Apr 2009

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Schrodinger equation
Nonlinear Schrodinger Equation
Homotopy Analysis Method
Series Solution
Taylor series
Schrodinger Equation
Analytical Methods
Nonlinear Problem
Exact Solution

Keywords

  • Analytical solution
  • Homotopy analysis method
  • Schrodinger equation
  • Series solution

ASJC Scopus subject areas

  • Modelling and Simulation
  • Numerical Analysis
  • Applied Mathematics

Cite this

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abstract = "In this paper, by means of the homotopy analysis method (HAM), the solutions of some Schrodinger equations are exactly obtained in the form of convergent Taylor series. The HAM contains the auxiliary parameter ℏ, that provides a convenient way of controlling the convergent region of series solutions. This analytical method is employed to solve linear and nonlinear examples to obtain the exact solutions. HAM is a powerful and easy-to-use analytic tool for nonlinear problems.",
keywords = "Analytical solution, Homotopy analysis method, Schrodinger equation, Series solution",
author = "Alomari, {A. K.} and {Md. Noorani}, {Mohd. Salmi} and {Mohd. Nazar}, Roslinda",
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AU - Alomari, A. K.

AU - Md. Noorani, Mohd. Salmi

AU - Mohd. Nazar, Roslinda

PY - 2009/4

Y1 - 2009/4

N2 - In this paper, by means of the homotopy analysis method (HAM), the solutions of some Schrodinger equations are exactly obtained in the form of convergent Taylor series. The HAM contains the auxiliary parameter ℏ, that provides a convenient way of controlling the convergent region of series solutions. This analytical method is employed to solve linear and nonlinear examples to obtain the exact solutions. HAM is a powerful and easy-to-use analytic tool for nonlinear problems.

AB - In this paper, by means of the homotopy analysis method (HAM), the solutions of some Schrodinger equations are exactly obtained in the form of convergent Taylor series. The HAM contains the auxiliary parameter ℏ, that provides a convenient way of controlling the convergent region of series solutions. This analytical method is employed to solve linear and nonlinear examples to obtain the exact solutions. HAM is a powerful and easy-to-use analytic tool for nonlinear problems.

KW - Analytical solution

KW - Homotopy analysis method

KW - Schrodinger equation

KW - Series solution

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JO - Communications in Nonlinear Science and Numerical Simulation

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