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
Main Author: Li, Xing
Format: Journal Article
Language:English
Published: Taylor & Francis Group 01.08.2006
Subjects:
2000 Mathematics Subject Classifications: 30E25
Approximate solution
Complex splines
Doubly periodic Riemann boundary value problem
ISSN:1747-6933, 1747-6941
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Abstract 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.
AbstractList 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.
Author Li, Xing
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SubjectTerms 2000 Mathematics Subject Classifications: 30E25
Approximate solution
Complex splines
Doubly periodic Riemann boundary value problem
Title Spline approximate solution for doubly periodic Riemann boundary value problem
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