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{ERROR GROWTH IN CONSERVATIVE NUMERICAL METHODS\\
FOR THE NONLINEAR SCHROEDINGER EQUATION}

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{\bf A. Dur\'an} (Universidad de Valladolid, Spain)

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One of the relevant properties of numerical methods for integrating
time-dependent differential equations is the conservation of
physical quantities that remain constant during the evolution of
the system. Some recent results \cite{uno} show the influence of the
conservative nature of the algorithms on the accuracy of the
numerical solution.

We consider solitary wave problems for the Nonlinear Schroedinger
equation and show that, at leading order, the use of conservative
numerical schemes makes the error increase with time in a different
way from that for nonconservative methods. Numerical experiments are
presented.

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\subsubsection*{References:}
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\bibitem[1]{uno}  J. de Frutos, J.M. Sanz-Serna. {\em Accuracy and Conservation Properties in Numerical Integration: the Case of the Korteweg-de Vries Equation}. Numer. Math. 75: 421-445 (1997).
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