An iterative method for solving nonlinear Riemann-Hilbert problems

DOI10.1016/0377-0427(90)90014-QzbMath0705.65020OpenAlexW2015330530MaRDI QIDQ918120

Elias Wegert

Publication date: 1990

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

Full work available at URL: https://doi.org/10.1016/0377-0427(90)90014-q

zbMATH Keywords

singular integral equationslinearizationnumerical examplesconformal mappingfast Fourier transformiterative methodquadratic convergenceNewton methodnonlinear Riemann-Hilbert boundary value problem

Mathematics Subject Classification ID

General theory of numerical methods in complex analysis (potential theory, etc.) (65E05) Boundary value problems in the complex plane (30E25) Schwarz-Christoffel-type mappings (30C30)

Related Items

COLLISION DETECTION OPTIMIZATION IN A MULTI-PARTICLE SYSTEM ⋮ Computing the Hilbert transform using biorthogonal spline wavelets ⋮ Fast conformal mapping of an ellipse to a simply connected region ⋮ Discretized versions of Newton type iterative methods for conformal mapping ⋮ A general framework for solving Riemann-Hilbert problems numerically ⋮ The Riemann-Hilbert problem and the generalized Neumann kernel on multiply connected regions ⋮ Numerical solution of Riemann-Hilbert problems: Painlevé II ⋮ Iterative methods for discrete nonlinear Riemann-Hilbert problems ⋮ Non-linear rational Riemann-Hilbert-problems with circular target curves ⋮ Unsteady aerodynamics of porous aerofoils

Cites Work

• Convergence proofs and error estimates for an iterative method for conformal mapping
• Zur Unität der Lösung der Theodorsenschen Integralgleichung der konformen Abbildung
• An iterative method for conformal mapping
• The Newton method for solving the Theodorsen integral equation
• Numerical conformal mapping methods based on function conjugation
• A bang-bang theorem for optimization over spaces of analytic functions
• Discrete Riemann-Hilbert problems, interpolation of simply closed curves, and numerical conformal mapping
• Fast algorithms for the conjugate periodic function
• Landesman-Lazer's Type Boundary Value Problems for Holomorphic Functions
• Topological Methods for Strongly Nonlinear Riemann-Hilbert Problems for Holomorphic Functions
• Plane potential flow past a cylinder with porous surface
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