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IMA Journal of Applied Mathematics Advance Access originally published online on July 3, 2008
IMA Journal of Applied Mathematics 2009 74(1):62-73; doi:10.1093/imamat/hxn013
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© The Author 2008. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.

An alternating method for Cauchy problems for Helmholtz-type operators in non-homogeneous medium

B. Tomas Johansson{dagger}

School of Mathematics, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK

Vladimir A. Kozlov

Department of Mathematics, Linköping University, SE-581 83 Linköping, Sweden

{dagger} Email: b.t.johansson{at}bham.ac.uk

Received on October 23, 2007; Revision received February 7, 2008. Accepted on April 16, 2008

Kozlov & Maz'ya (1989, Algebra Anal., 1, 144–170) proposed an alternating iterative method for solving Cauchy problems for general strongly elliptic and formally self-adjoint systems. However, in many applied problems, operators appear that do not satisfy these requirements, e.g. Helmholtz-type operators. Therefore, in this study, an alternating procedure for solving Cauchy problems for self-adjoint non-coercive elliptic operators of second order is presented. A convergence proof of this procedure is given.

Keywords: Cauchy problem; Helmholtz equation.


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