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

DOI

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.

Copyright

© 2017, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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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  - Proceedings of the 2017 International Conference on Manufacturing Engineering and Intelligent Materials (ICMEIM 2017)
PB  - Atlantis Press
SP  - 180
EP  - 188
SN  - 2352-5401
UR  - https://doi.org/10.2991/icmeim-17.2017.32
DO  - 10.2991/icmeim-17.2017.32
ID  - Qian2017/02
ER  -