Journal ArticleDOI
Numerical solution of an integral equation with a logarithmic kernel
TLDR
In this article, an integral equation whose kernel is equal to the logarithm of the distance between two points on a plane, closed, smooth, and simple curve is replaced by a system of linear algebraic equations which can be solved numerically.Abstract:
When formulating boundary value problems within different branches of mathematical physics, one encounters an integral equation whose kernel is equal to the logarithm of the distance between two points on a plane, closed, smooth, and simple curve. This equation can be replaced by a system of linear algebraic equations which can be solved numerically.read more
Citations
More filters
Journal ArticleDOI
Quadrature methods for periodic singular and weakly singular Fredholm integral equations
Avram Sidi,Mosha Israeli +1 more
TL;DR: High-accuracy numerical quadrature methods for integrals of singular periodic functions are proposed based on the appropriate Euler-Maclaurin expansions of trapezoidal rule approximations and their extrapolations for singular and weakly singular Fredholm integral equations.
Journal ArticleDOI
A Galerkin collocation method for some integral equations of the first kind
TL;DR: A certain modified collocation method which is a fully discretized numerical method for the solution of Fredholm integral equations of the first kind with logarithmic kernel as principal part is presented.
Journal ArticleDOI
On the asymptotic convergence of collocation methods with spline functions of even degree
J. Saranen,Wolfgang L. Wendland +1 more
TL;DR: In this paper, the authors investigated the asymptotic convergence of the collocation method using even-degree polynomial splines applied to strongly elliptic systems of pseudo-differential equations on closed curves with convolutional principal part.
Journal ArticleDOI
A meshless discrete Galerkin (MDG) method for the numerical solution of integral equations with logarithmic kernels
TL;DR: The numerical scheme developed in the current paper utilizes the non-uniform Gauss–Legendre quadrature rule for approximating logarithm-like singular integrals and so reduces the solution of theLogarithmic integral equation to the Solution of a linear system of algebraic equations.
Journal ArticleDOI
The convergence of even degree spline collocation solution for potential problems in smooth domains of the plane
TL;DR: In this article, the authors derived new error estimates for collocation solution of potential type problems by using even degree smooth splines as trial functions and showed that for smooth potentials the assured convergence is of the same order as by using splines of the odd degreed+1.
References
More filters
Book
Table of Integrals, Series, and Products
TL;DR: Combinations involving trigonometric and hyperbolic functions and power 5 Indefinite Integrals of Special Functions 6 Definite Integral Integral Functions 7.Associated Legendre Functions 8 Special Functions 9 Hypergeometric Functions 10 Vector Field Theory 11 Algebraic Inequalities 12 Integral Inequality 13 Matrices and related results 14 Determinants 15 Norms 16 Ordinary differential equations 17 Fourier, Laplace, and Mellin Transforms 18 The z-transform
Related Papers (5)
On the numerical treatment of the singular integral equation of the second kind
M. A. Abdou,A. A. Nasr +1 more