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

Authors:
U. Al Khawaja;Kamel Al-Khaled
Affiliations:
Department of Physics, United Arab Emirates University, Al-Ain, U.A.E.;Department of Mathematics, Jordan University of Science and Technology, IRBID, Jordan
Venue:
International Journal of Computer Mathematics
Year:
2007

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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.