| Title:
|
On the asymptotic convergence of the polynomial collocation method for singular integral equations and periodic pseudodifferential equations (English) |
| Author:
|
Fedotov, A. I. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
38 |
| Issue:
|
1 |
| Year:
|
2002 |
| Pages:
|
1-13 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We prove the convergence of polynomial collocation method for periodic singular integral, pseudodifferential and the systems of pseudodifferential equations in Sobolev spaces $H^{s}$ via the equivalence between the collocation and modified Galerkin methods. The boundness of the Lagrange interpolation operator in this spaces when $s>1/2$ allows to obtain the optimal error estimate for the approximate solution i.e. it has the same rate as the best approximation of the exact solution by the polynomials. (English) |
| Keyword:
|
singular integral equations |
| Keyword:
|
periodic pseudodifferential equations |
| Keyword:
|
Galerkin method |
| Keyword:
|
collocation method |
| MSC:
|
45E05 |
| MSC:
|
47G30 |
| MSC:
|
65N35 |
| MSC:
|
65R20 |
| idZBL:
|
Zbl 1087.65109 |
| idMR:
|
MR1899563 |
| . |
| Date available:
|
2008-06-06T22:29:35Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107814 |
| . |
| Reference:
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