On the numerical solution of two-dimensional singular integral equation

2006 ◽  
Vol 173 (1) ◽  
pp. 389-393 ◽  
Author(s):  
A.S. Ismail
Keyword(s):  
Integral Equation ◽  
Singular Integral Equation ◽  
Numerical Solution ◽  
Singular Integral ◽  
Two Dimensional

Elasticity Solution of Deep Beam Under Settlement of Supports

1976 ◽  
Vol 43 (4) ◽  
pp. 613-618 ◽  
Author(s):  
S. N. Prasad ◽  
P. K. Chiu
Keyword(s):  
Integral Equation ◽  
Singular Integral Equation ◽  
Singular Integral ◽  
The Other ◽  
Tangential Displacement ◽  
Deep Beam ◽  
Two Dimensional ◽  
Singular Behavior ◽  
Elasticity Solution ◽  
Collocation Technique

The present study investigates the two-dimensional stresses and displacements in a finite rectangle whose one set of parallel edges is given a relative tangential displacement by means of rigidly attached planes. The other set of parallel edges is free from tractions. The problem is formulated in terms of a singular integral equation of the first kind, which yields the correct singular behavior of stresses at the corners. The integral equation is solved numerically by employing Gauss-Jacobi quadrature in conjunction with certain collocation technique. Numerical results of quantities of practical interests are shown graphically and also compared with the classical bending analysis.

scholarly journals Numerical solution of a weakly singular integral equation by the method of orthogonal polynomials

2021 ◽  
pp. 98-103
Author(s):  
Sergei M. Sheshko
Keyword(s):  
Integral Equation ◽  
Approximate Solution ◽  
Singular Integral Equation ◽  
Orthogonal Polynomials ◽  
Numerical Solution ◽  
Singular Integral ◽  
Algebraic Equations ◽  
Linear Algebraic Equations ◽  
Expansion Coefficients ◽  
Analytical Expressions

A scheme is constructed for the numerical solution of a singular integral equation with a logarithmic kernel by the method of orthogonal polynomials. The proposed schemes for an approximate solution of the problem are based on the representation of the solution function in the form of a linear combination of the Chebyshev orthogonal polynomials and spectral relations that allows to obtain simple analytical expressions for the singular component of the equation. The expansion coefficients of the solution in terms of the Chebyshev polynomial basis are calculated by solving a system of linear algebraic equations. The results of numerical experiments show that on a grid of 20 –30 points, the error of the approximate solution reaches the minimum limit due to the error in representing real floating-point numbers.

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