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

B. Tomas Johansson; Vladimir A. Kozlov

doi:10.1093/imamat/hxn013

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

B. Tomas Johansson, Vladimir A. Kozlov

Research output: Contribution to journal › Article › peer-review

13 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	62-73
Number of pages	12
Journal	IMA Journal of Applied Mathematics
Volume	74
Issue number	1
Early online date	3 Jul 2008
DOIs	https://doi.org/10.1093/imamat/hxn013
Publication status	Published - 2009

Keywords

Cauchy problem
Helmholtz equation

Access to Document

10.1093/imamat/hxn013

Cite this

@article{af09faedc29c4cd08e4df9b32b7cb34a,

title = "An alternating method for Cauchy problems for Helmholtz-type operators in non-homogeneous medium",

abstract = "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",

author = "Johansson, {B. Tomas} and Kozlov, {Vladimir A.}",

year = "2009",

doi = "10.1093/imamat/hxn013",

language = "English",

volume = "74",

pages = "62--73",

journal = "IMA Journal of Applied Mathematics",

issn = "0272-4960",

publisher = "Oxford University Press",

number = "1",

}

TY - JOUR

T1 - An alternating method for Cauchy problems for Helmholtz-type operators in non-homogeneous medium

AU - Johansson, B. Tomas

AU - Kozlov, Vladimir A.

PY - 2009

Y1 - 2009

N2 - 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.

AB - 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.

KW - Cauchy problem

KW - Helmholtz equation

UR - https://academic.oup.com/imamat/article/74/1/62/742691

U2 - 10.1093/imamat/hxn013

DO - 10.1093/imamat/hxn013

M3 - Article

SN - 0272-4960

VL - 74

SP - 62

EP - 73

JO - IMA Journal of Applied Mathematics

JF - IMA Journal of Applied Mathematics

IS - 1

ER -

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

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this