The convergence of even degree spline collocation solution for potential problems in smooth domains of the plane

DOI10.1007/BF01397549zbMath0628.65107OpenAlexW2075477953MaRDI QIDQ1093336

Jukka Saranen

Publication date: 1988

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/133288

zbMATH Keywords

convergencenumerical exampleerror estimatescollocationpotential problemeven degree smooth splines

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Numerical methods for integral equations (65R20) Boundary value problems for higher-order elliptic equations (35J40) Integral representations of solutions to PDEs (35C15) Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) (45E10) Biharmonic, polyharmonic functions and equations, Poisson's equation in two dimensions (31A30)

Related Items (16)

A piecewise constant collocation method using cosine mesh grading for Symm's equation ⋮ Fully-discrete collocation methods for an integral equation of the first kind ⋮ Orthogonal collocation in the nonconforming boundary element method ⋮ A quadrature-based approach to improving the collocation method ⋮ Semi-discrete Galerkin approximations for the single-layer equation on Lipschitz curves ⋮ \(L^ p\) estimates of boundary integral equations for some nonlinear boundary value problems ⋮ Spline qualocation methods for boundary integral equations ⋮ Double layer potential scheme for Dirichlet problems on smooth open arcs ⋮ Extrapolation techniques and the collocation method for a class of boundary integral equations ⋮ The modified quadrature method for logarithmic-kernel integral equations on closed curves ⋮ Midpoint collocation for Cauchy singular integral equations ⋮ Spline collocation for strongly elliptic equations on the torus ⋮ From finite differences to finite elements. A short history of numerical analysis of partial differential equations ⋮ Fast isogeometric boundary element method based on independent field approximation ⋮ Extrapolation methods for spline collocation solutions of pseudodifferential equations on curves ⋮ The \(K\)-operator and the qualocation method for strongly elliptic equations on smooth curves

Cites Work

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• Ein Lokalisierungsprinzip in der Theorie der Spline-Approximationen und einige Anwendungen
• On the Asymptotic Convergence of Collocation Methods With Spline Functions of Even Degree
• SPLINE APPROXIMATION OF SINGULAR INTEGRAL EQUATIONS
• Konstruktive Methoden der konformen Abbildung
• Numerical solution of an integral equation with a logarithmic kernel
• An Improved Method for Numerical Conformal Mapping
• The Eigenvalue Problem for a Pair of Coupled Integral Equations Arising in the Numerical Solution of Laplace’s Equation

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