Proceedings of the 2017 International Conference on Manufacturing Engineering and Intelligent Materials (ICMEIM 2017)

Optimal Error Bound and A Semi-discrete Difference Scheme for the Cauchy Problem of the Modified Helmholtz Equation

Authors
Ai-lin Qian, Zi-min Chen
Corresponding Author
Ai-lin Qian
Available Online February 2017.
DOI
https://doi.org/10.2991/icmeim-17.2017.32How to use a DOI?
Keywords
Ill-posed Problems, The Cauchy Problem of Helmholtz Equation, Difference Schemes, Regularization
Abstract
The Cauchy problem of Helmholtz equation is severely ill-posed problem. In this paper, we consider the Cauchy problem for the Helmholtz equation where the Cauchy data is given at and the solution is sought in the interval . A semi-discrete difference schemes together with a choice of regularization parameter is presented and error estimate is obtained. The numerical example shows the effectiveness of this method.
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Proceedings
2017 International Conference on Manufacturing Engineering and Intelligent Materials (ICMEIM 2017)
Part of series
Advances in Engineering Research
Publication Date
February 2017
ISBN
978-94-6252-317-3
ISSN
2352-5401
DOI
https://doi.org/10.2991/icmeim-17.2017.32How to use a DOI?
Open Access
This is an open access article distributed under the CC BY-NC license.

Cite this article

TY  - CONF
AU  - Ai-lin Qian
AU  - Zi-min Chen
PY  - 2017/02
DA  - 2017/02
TI  - Optimal Error Bound and A Semi-discrete Difference Scheme for the Cauchy Problem of the Modified Helmholtz Equation
BT  - 2017 International Conference on Manufacturing Engineering and Intelligent Materials (ICMEIM 2017)
PB  - Atlantis Press
SN  - 2352-5401
UR  - https://doi.org/10.2991/icmeim-17.2017.32
DO  - https://doi.org/10.2991/icmeim-17.2017.32
ID  - Qian2017/02
ER  -