On the asymptotic convergence of a collocation method for some boundary integral equations of the first kind

• Published in: Journal of computational and applied mathematics Vol. 78; no. 2; pp. 329 - 353
• Main Author: Abou El-Seoud, M.S.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 17.02.1997; Elsevier
• Subjects: Absolute and relative error; Boundary integral equation; Collocation and Galerkin-collocation method; Discrete maximum norm; Exact sciences and technology; Finite element function; Hölder and Sobolev spaces; Mathematics; Matrix norm; Numerical analysis; Numerical analysis. Scientific computation; Numerical approximation; Numerical linear algebra; Numerical methods in mathematical programming; Numerical methods in mathematical programming, optimization and calculus of variations; Numerical methods in optimization and calculus of variations; Numerical methods in probability and statistics; One-, three-and nine-point quadrature formulas; Ordinary differential equations; Sciences and techniques of general use; Spline polynomial; 65R20; Finite element function; 65N38; Hölder and Sobolev spaces; Matrix norm; Spline polynomial; Discrete maximum norm; One-, three-and nine-point quadrature formulas; Collocation and Galerkin-collocation method; 65F10; 65L60; Boundary integral equation; 65D32; Absolute and relative error; 65N22; 65D07; 65L10; 65N30; Finite element method; Convergence of numerical methods; Boundary value problems; Error estimation; Integral equations; Singular equation; Numerical methods; Boundary integral method; Relative error; Quadrature formula; Collocation method; Spline approximation
• ISSN: 0377-0427; 1879-1778
• DOI: 10.1016/S0377-0427(97)00161-1

In this paper we present a certain collocation method for the numerical solution of a class of boundary integral equations of the first kind with logarithmic kernel as principle part. The transformation of the boundary value problem into boundary singular integral equation of the first kind via single-layer potential is discussed. A discretization and error representation for the numerical solution of boundary integral equations has been given. Quadrature formulae have been proposed and the error arising due to the quadrature formulae used has been estimated. The convergence of the solution with respect to the proposed numerical algorithm is shown and finally some numerical results have been presented.