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 Num. Meth. Prog., 2008, Volume 9, Issue 2, Pages 163–169 (Mi vmp430)

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On the stability of the Cauchy problem for the Helmholtz equation in a three-dimensional cylinder

A. N. Demidovaa, Ya. M. Zhileikinb

a Institute of Cryptography, Communications and Informatics, Academy of Federal Security Service of Russian Federation, Moscow
b Lomonosov Moscow State University, Research Computing Center

Abstract: Some stability conditions for the solution to the Cauchy problem for the Helmholtz equation are proposed and substantiated for initial data in relation to the spectral distribution of initial functions and their perturbations. The problem is considered in a semi-infinite three-dimensional cylinder. The stability of a finite-difference scheme used to solve the Cauchy problem for the Helmholtz equation in a three-dimensional rectangular cylinder is studied. Several constraints imposed on the steps of this finite-difference scheme to ensure its stability are obtained.

Keywords: Helmholtz equation, Cauchy problem, stability with respect to initial data, finite-difference schemes, wave equations.

Full text: PDF file (147 kB)
UDC: 517.955.2

Citation: A. N. Demidova, Ya. M. Zhileikin, “On the stability of the Cauchy problem for the Helmholtz equation in a three-dimensional cylinder”, Num. Meth. Prog., 9:2 (2008), 163–169

Citation in format AMSBIB
\Bibitem{DemZhi08} \by A.~N.~Demidova, Ya.~M.~Zhileikin \paper On the stability of the Cauchy problem for the Helmholtz equation in a three-dimensional cylinder \jour Num. Meth. Prog. \yr 2008 \vol 9 \issue 2 \pages 163--169 \mathnet{http://mi.mathnet.ru/vmp430}