An extrapolation method for a class of boundary integral equations

DOI10.1090/S0025-5718-96-00723-5zbMath0851.65077MaRDI QIDQ4878569

Yuesheng Xu, Yun-He Zhao

Publication date: 26 November 1996

Published in: Mathematics of Computation (Search for Journal in Brave)

zbMATH Keywords

extrapolation methodboundary integral equationsNyström methodLaplace's equationsecond kindlogarithmic kernel functionperiodic Fredholm integral equations

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Integral representations of solutions to PDEs (35C15) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Boundary element methods for boundary value problems involving PDEs (65N38)

Related Items (11)

Asymptotic error expansions for hypersingular integrals ⋮ Mechanical quadrature methods and extrapolation algorithms for boundary integral equations with linear boundary conditions in elasticity ⋮ Computing the Newton potential in the boundary integral equation for the Dirichlet problem of the Poisson equation ⋮ Extrapolation algorithms for solving nonlinear boundary integral equations by mechanical quadrature methods ⋮ A fast Fourier-Galerkin method solving boundary integral equations for the Helmholtz equation with exponential convergence ⋮ Extrapolation and superconvergence of the Steklov eigenvalue problem ⋮ Asymptotic error analysis of a quadrature method for integral equations with Green's function kernels ⋮ Fast Fourier-Galerkin methods for solving singular boundary integral equations: Numerical integration and precondition ⋮ A fully discrete fast Fourier-Galerkin method solving a boundary integral equation for the biharmonic equation ⋮ Mechanical quadrature methods and their splitting extrapolations for boundary integral equations of first kind on open arcs ⋮ Richardson extrapolation applied to boundary element method results in a Dirichlet problem for the Laplace equation

Cites Work

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• On the boundary element method for some nonlinear boundary value problems
• Quadrature methods for periodic singular and weakly singular Fredholm integral equations
• Regularity of the solution to a class of weakly singular Fredholm integral equations of the second kind
• Comparison of some numerical quadrature formulas for weakly singular periodic Fredholm integral equations
• The numerical solution of Fredholm integral equations of the second kind with singular kernels
• An Extension of the Euler-Maclaurin Summation Formula to Functions with a Branch Singularity
• Boundary Integral Equation Methods for Solving Laplace's Equation with Nonlinear Boundary Conditions: The Smooth Boundary Case
• An Algorithm for a Generalization of the Richardson Extrapolation Process
• A Further Extension of the Euler-Maclaurin Summation Formula

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