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SUMMARY:A. D. Yunakovsky
DTSTART:20221208T110000Z
DTEND:20221208T120000Z
DTSTAMP:20260423T022843Z
UID:mmandim/48
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/48/"
 >Methods for numerical simulation of NLS</a>\nby A. D. Yunakovsky as part 
 of Mathematical models and integration methods\n\n\nAbstract\nThe advent o
 f supercomputers made it possible to model multidimensional NLS and reveal
 ed new problems: new parallelizable algorithms were required.\n\nFor equat
 ions of the "parabolic" type\, which include the non-stationary Schröding
 er equation\, numerical schemes have very stringent stability conditions: 
 $\\Delta t < \\Delta x^2$\, which\, in fact\, slows down the solution of t
 he problem when the grid is refined. In addition\, in equations of the NLS
 E type\, high spatial harmonics do not decay with time\, but have rapidly 
 changing phases\, which leads even under a "relatively mild" condition of 
 stability to the phenomenon of random phases.\n\nA review of grid and spec
 tral methods for finding approximate solutions of the NSE is given\, and t
 he possibilities of using the FFT are analyzed. The problem of increasing 
 the counting step with respect to time and typical errors are discussed. B
 rief reviews of the use of the operator exponential method and the method 
 of nonreflecting boundary conditions are given. The possibilities of the h
 yperbolization method for NLS are discussed.\n
LOCATION:https://researchseminars.org/talk/mmandim/48/
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