Abstract
This paper devises a computational method for solving a Cauchy problem of Laplace's equation in multidimensional space, By using the Green formula, the Cauchy problem is transformed to a moment problem so that numerical computations using a regularization technique can be achieved. A stability estimation and a suitable choice of regularization parameter for the proposed method are also given. For numerical verification, a numerical example in the three-dimensional case is presented.
| Original language | English |
|---|---|
| Pages (from-to) | 381-396 |
| Journal | SIAM Journal on Control and Optimization |
| Volume | 42 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 2003 |
Research Keywords
- Cauchy problem
- Ill-posedness
- Multidimension
- Numerical computation
Publisher's Copyright Statement
- COPYRIGHT TERMS OF DEPOSITED FINAL PUBLISHED VERSION FILE: © 2003 Society for Industrial and Applied Mathematics.
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