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On one semidiscrete Galerkin method for a generalized time-dependent 2D Schrödinger equation

✍ Scribed by A. Zlotnik; B. Ducomet; H. Goutte; J.F. Berger

Publisher
Elsevier Science
Year
2009
Tongue
English
Weight
544 KB
Volume
22
Category
Article
ISSN
0893-9659

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✦ Synopsis

An initial-boundary value problem for a generalized 2D Schrödinger equation in a rectangular domain is considered. Approximate solutions of the form

) are treated, where χ 1 , . . . , χ N are the first N eigenfunctions of a 1D eigenvalue problem in x 2 depending parametrically on x 1 and c 1 , . . . , c N are coefficients to be defined; they are of interest for nuclear physics problems. The corresponding semidiscrete Galerkin approximate problem is stated and analyzed. Uniform-in-time error bounds of arbitrarily high orders O N -θ log N in L 2 and O N -(θ-1) log 1/2 N in H 1 , θ > 1, are proved.

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