عنوان مجله
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Iranian Journal of Mathematical Sciences and Informatics
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کلیدواژهها
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Phase-lag, Schrodinger equation, Numerical solution, Newton-
Cotes formulae, Derivative.
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چکیده
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In this paper, we investigate the connection between closed
Newton-Cotes formulae, trigonometrically-fitted methods, symplectic integrators
and efficient integration of the Schr¨odinger equation. The study
of multistep symplectic integrators is very poor although in the last
decades several one step symplectic integrators have been produced based
on symplectic geometry (see the relevant literature and the references
here). In this paper, we study the closed Newton-Cotes formulae and
we write them as symplectic multilayer structures. Based on the closed
Newton-Cotes formulae, we also develop trigonometrically-fitted symplectic
methods. An error analysis for the one-dimensional Schr¨odinger equation
of the new developed methods and a comparison with previous developed
methods is also given. We apply the new symplectic schemes to
the well-known radial Schr¨odinger equation in order to investigate the
efficiency of the proposed method to these type of problems.
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