| Title | Features of the Nyström method for the Sherman-Lauricella equation on Piecewise Smooth Curves |
| Authors | Victor Didenko, Johan Helsing |
| Alternative Location | http://www.maths.lth.se/na/... |
| Alternative Location | http://dx.doi.org/10.4208/e..., Restricted Access |
| Publication | East Asian Journal on Applied Mathematics |
| Year | 2011 |
| Volume | 1 |
| Issue | 4 |
| Pages | 403 - 414 |
| Document type | Article |
| Status | Published |
| Quality controlled | Yes |
| Language | eng |
| Publisher | Global Science Press |
| Abstract English | The stability of the Nyström method for the Sherman-Lauricella equation on contours with corner points $c_j$, $j=0,1,...,m$ relies on the invertibility of certain operators $A_{c_j}$ belonging to an algebra of Toeplitz operators. The operators $A_{c_j}$ do not depend on the shape of the contour, but on the opening angle $\theta_j$ of the corresponding corner $c_j$ and on parameters of the approximation method mentioned. They have a complicated structure and there is no analytic tool to verify their invertibility. To study this problem, the original Nyström method is applied to the Sherman-Lauricella equation on a special model contour that has only one corner point with varying opening angle $\theta_j$. In the interval $(0.1\pi,1.9\pi)$, it is found that there are $8$ values of $\theta_j$ where the invertibility of the operator $A_{c_j}$ may fail, so the corresponding original Nyström method on any contour with corner points of such magnitude cannot be stable and requires modification. |
| Keywords | Sherman-Lauricella equation, Nyström method, stability, |
| ISBN/ISSN/Other | ISSN: 2079-7370 (online) |
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Last update: 2013-04-11
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