A boundary integral method for the Riemann–Hilbert problem in domains with corners

DOI10.1080/17476930802335080zbMath1159.30023OpenAlexW2112155935MaRDI QIDQ3548418

Zamzana Zamzamir, Ali Hassan Mohamed Murid, Mohamed M. S. Nasser

Publication date: 12 December 2008

Published in: Complex Variables and Elliptic Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/17476930802335080

zbMATH Keywords

Fredholm integral equationsRiemann-Hilbert problemgeneralized Neumann kernelpiecewise smooth boundary

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Boundary value problems in the complex plane (30E25) Fredholm integral equations (45B05)

Related Items (14)

Fast computing of conformal mapping and its inverse of bounded multiply connected regions onto second, third and fourth categories of Koebe's canonical slit regions ⋮ Computation of conformal invariants ⋮ Polycircular domains, numerical conformal mappings, and moduli of quadrilaterals ⋮ Boundary integral equations with the generalized Neumann kernel for Laplace's equation in multiply connected regions ⋮ Fast and accurate computation of the logarithmic capacity of compact sets ⋮ A boundary integral equation with the generalized Neumann kernel for a certain class of mixed boundary value problem ⋮ A Boundary Integral Method for the General Conjugation Problem in Multiply Connected Circle Domains ⋮ A boundary integral equation with the generalized Neumann kernel for a mixed boundary value problem in unbounded multiply connected regions ⋮ Conformal invariants in simply connected domains ⋮ A fast numerical method for ideal fluid flow in domains with multiple stirrers ⋮ Numerical conformal mapping of multiply connected regions onto the second, third and fourth categories of Koebe's canonical slit domains ⋮ Numerical conformal mapping and its inverse of unbounded multiply connected regions onto logarithmic spiral slit regions and straight slit regions ⋮ Straight slits map and its inverse of bounded multiply connected regions ⋮ Fast computation of the circular map

Cites Work

• The Riemann--Hilbert problem and the generalized Neumann kernel
• A Nyström method for boundary integral equations in domains with corners
• A sinc quadrature method for the double-layer integral equation in planar domains with corners
• An optimal order collocation method for first kind boundary integral equations on polygons
• A quadrature method for the Cauchy singular integral equations
• The Riemann-Hilbert problem and the generalized Neumann kernel on multiply connected regions
• The Numerical Solution of Laplace's Equation on a Wedge

This page was built for publication: A boundary integral method for the Riemann–Hilbert problem in domains with corners