Spline approximate solution for doubly periodic Riemann boundary value problem
A straightforward method for the approximate solution of doubly periodic Riemann boundary value problems for analytic functions is proposed through the approximation by the δ-cardinal splines of the first degree and the cubic δ-cardinal splines. First, we approximate the solution of the doubly perio...
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| Vydáno v: | Complex variables and elliptic equations Ročník 51; číslo 8-11; s. 1047 - 1058 |
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| Hlavní autor: | |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Taylor & Francis Group
01.08.2006
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| Témata: | |
| ISSN: | 1747-6933, 1747-6941 |
| On-line přístup: | Získat plný text |
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| Shrnutí: | A straightforward method for the approximate solution of doubly periodic Riemann boundary value problems for analytic functions is proposed through the approximation by the δ-cardinal splines of the first degree and the cubic δ-cardinal splines. First, we approximate the solution of the doubly periodic Riemann jump problem based on approximation of the singular integral operator with Weierstrass ζ-function kernel. Furthermore we obtain the approximate solution of the general non-homogenous doubly periodic Riemann problem. We prove that the approximate solution is sufficiently close to the exact solution in any degree when the partition Δ is sufficiently fine.
†Dedicated to Professor Guochun Wen on his 75th anniversary. |
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| ISSN: | 1747-6933 1747-6941 |
| DOI: | 10.1080/17476930600740887 |