Optimal Error Bound and A Semi-discrete Difference Scheme for the Cauchy Problem of the Modified Helmholtz Equation
Ai-lin Qian, Zi-min Chen
Available Online February 2017.
- https://doi.org/10.2991/icmeim-17.2017.32How to use a DOI?
- Ill-posed Problems, The Cauchy Problem of Helmholtz Equation, Difference Schemes, Regularization
- 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.
- 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 SP - 180 EP - 188 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 -