The Riemann-Hilbert problem and the generalized Neumann kernel on multiply connected regions

DOI10.1016/j.cam.2007.01.021zbMath1157.45303OpenAlexW2000915675MaRDI QIDQ2479368

Mohamed M. S. Nasser, Rudolf Wegmann

Publication date: 26 March 2008

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2007.01.021

zbMATH Keywords

Fredholm integral equationsRiemann-Hilbert problemsgeneralized Neumann kernelmultiply connected regions

Mathematics Subject Classification ID

Boundary value problems in the complex plane (30E25) Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) (45E10)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The Riemann--Hilbert problem and the generalized Neumann kernel
• Convergence proofs and error estimates for an iterative method for conformal mapping
• An iterative method for solving nonlinear Riemann-Hilbert problems
• Eigenproblem of the generalized Neumann kernel
• The Numerical Solution of Fredholm integral Equations of the Second Kind
• The Deferred Approach to the Limit for Eigenvalues of Integral Equations
• Fast conformal mapping of multiply connected regions

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