Name
Title | ||
|---|---|---|
A quasi-reversibility regularization method for the Cauchy problem of the Helmholtz equation |
Abstract | ||
|---|---|---|
In this paper, a Cauchy problem for the Helmholtz equation is considered. It is known that such a problem is severely ill-posed, i.e. the solution does not depend continuously on the given Cauchy data. We propose a quasi-reversibility regularization method to solve it. Convergence estimates are established under two different a priori assumptions for an exact solution. Numerical results obtained by two different schemes show that our proposed methods work well. |
Year | DOI | Venue |
|---|---|---|
2011 | 10.1080/00207160.2010.482986 | Int. J. Comput. Math. |
Keywords | Field | DocType |
exact solution,convergence estimate,different scheme,numerical result,helmholtz equation,cauchy data,quasi-reversibility regularization method,cauchy problem | Cauchy problem,Convergence (routing),Mathematical optimization,Mathematical analysis,Backus–Gilbert method,Cauchy distribution,Regularization (mathematics),Helmholtz equation,Initial value problem,Cauchy's convergence test,Mathematics | Journal |
Volume | Issue | ISSN |
88 | 4 | 0020-7160 |
Citations | PageRank | References |
1 | 0.60 | 1 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| H. W. Zhang | 1 | 5 | 2.57 |
| H. H. Qin | 2 | 1 | 0.94 |
| T. Wei | 3 | 87 | 18.96 |