Name
Title | ||
|---|---|---|
Convergence analysis for the Cauchy problem of Laplace's equation by a regularized method of fundamental solutions |
Abstract | ||
|---|---|---|
In this paper, we consider the Cauchy problem of Laplace's equation in the neighborhood of a circle. The method of fundamental solutions (MFS) combined with the discrete Tikhonov regularization is applied to obtain a regularized solution from noisy Cauchy data. Under the suitable choices of a regularization parameter and an a priori assumption to the Cauchy data, we obtain a convergence result for the regularized solution. Numerical experiments are presented to show the effectiveness of the proposed method. |
Year | DOI | Venue |
|---|---|---|
2010 | 10.1007/s10444-009-9134-7 | Adv. Comput. Math. |
Keywords | Field | DocType |
The method of fundament solutions,Cauchy problem for the Laplace’s equation,Tikhonov regularization,Convergence analysis,65M32,65M12 | Tikhonov regularization,Cauchy problem,Mathematical optimization,Mathematical analysis,Backus–Gilbert method,Laplace's equation,Cauchy distribution,Cauchy boundary condition,Method of fundamental solutions,Cauchy's convergence test,Mathematics | Journal |
Volume | Issue | ISSN |
33 | 4 | 1019-7168 |
Citations | PageRank | References |
2 | 0.51 | 3 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| T. Wei | 1 | 87 | 18.96 |
| D. Y. Zhou | 2 | 2 | 0.51 |