Error control in Adomian's decomposition method applied to the time-dependent Gross-Pitaevskii equation

U. Al Khawaja; Kamel Al-Khaled

doi:10.1080/00207160601173589

Error control in Adomian's decomposition method applied to the time-dependent Gross-Pitaevskii equation

U. Al Khawaja^*, Kamel Al-Khaled

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

We apply the Adomian decomposition method to the one-dimensional time-dependent Gross-Pitaevskii equation, which describes the evolution of bright solitons. We investigate the behaviour of the error in the solutions obtained by the Adominan method and make a comparison with the exact solution. We obtain a formula for the error as a function of time and the number of Adomian polynomials used.

Original language	English
Pages (from-to)	81-87
Number of pages	7
Journal	International Journal of Computer Mathematics
Volume	84
Issue number	1
DOIs	https://doi.org/10.1080/00207160601173589
Publication status	Published - Jan 2007
Externally published	Yes

Keywords

Gross-Pitaevskii equation
Numerical methods
Solitary wave solutions

ASJC Scopus subject areas

Computer Science Applications
Computational Theory and Mathematics
Applied Mathematics

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10.1080/00207160601173589

Cite this

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abstract = "We apply the Adomian decomposition method to the one-dimensional time-dependent Gross-Pitaevskii equation, which describes the evolution of bright solitons. We investigate the behaviour of the error in the solutions obtained by the Adominan method and make a comparison with the exact solution. We obtain a formula for the error as a function of time and the number of Adomian polynomials used.",

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author = "{Al Khawaja}, U. and Kamel Al-Khaled",

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AU - Al-Khaled, Kamel

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AB - We apply the Adomian decomposition method to the one-dimensional time-dependent Gross-Pitaevskii equation, which describes the evolution of bright solitons. We investigate the behaviour of the error in the solutions obtained by the Adominan method and make a comparison with the exact solution. We obtain a formula for the error as a function of time and the number of Adomian polynomials used.

KW - Gross-Pitaevskii equation

KW - Numerical methods

KW - Solitary wave solutions

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Error control in Adomian's decomposition method applied to the time-dependent Gross-Pitaevskii equation

Abstract

Keywords

ASJC Scopus subject areas

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