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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| Published in: | Complex variables and elliptic equations Vol. 51; no. 8-11; pp. 1047 - 1058 |
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| Main Author: | |
| Format: | Journal Article |
| Language: | English |
| Published: |
Taylor & Francis Group
01.08.2006
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| Subjects: | |
| ISSN: | 1747-6933, 1747-6941 |
| Online Access: | Get full text |
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| Summary: | 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 |