scholarly journals On solving singular integral equations via a hyperbolic tangent quadrature rule

1986 ◽  
Vol 47 (175) ◽  
pp. 159-159 ◽  
Author(s):  
Ezio Venturino
Keyword(s):  
Integral Equations ◽  
Singular Integral ◽  
Singular Integral Equations ◽  
Quadrature Rule ◽  
Hyperbolic Tangent

scholarly journals Solution of Cauchy-Type Singular Integral Equations of the First Kind with Zeros of Jacobi Polynomials as Interpolation Nodes

2007 ◽  
Vol 2007 ◽  
pp. 1-12 ◽  
Author(s):  
G. E. Okecha
Keyword(s):  
Integral Equations ◽  
Singular Integral ◽  
Jacobi Polynomials ◽  
Singular Integral Equations ◽  
Quadrature Rule ◽  
Convergence Result ◽  
Cauchy Type ◽  
Algebraic Equations ◽  
Linear Algebraic Equations ◽  
Lagrangian Interpolation

Of concern in this paper is the numerical solution of Cauchy-type singular integral equations of the first kind at a discrete set of points. A quadrature rule based on Lagrangian interpolation, with the zeros of Jacobi polynomials as nodes, is developed to solve these equations. The problem is reduced to a system of linear algebraic equations. A theoretical convergence result for the approximation is provided. A few numerical results are given to illustrate and validate the power of the method developed. Our method is more accurate than some earlier methods developed to tackle this problem.

scholarly journals Convergence analysis of the generalized Euler-Maclaurin quadrature rule for solving weakly singular integral equations

Filomat ◽  
2019 ◽  
Vol 33 (6) ◽  
pp. 1801-1815
Author(s):  
Grzegorz Rządkowski ◽  
Emran Tohidi
Keyword(s):  
Numerical Solution ◽  
Convergence Analysis ◽  
Integral Equations ◽  
Singular Integral ◽  
Singular Integral Equations ◽  
Quadrature Rule ◽  
Summation Formula ◽  
Volterra Integral Equations ◽  
Weakly Singular ◽  
Weakly Singular Integral Equations

In the present paper we use the generalized Euler-Maclaurin summation formula to study the convergence and to solve weakly singular Fredholm and Volterra integral equations. Since these equations have different nature, the proposed convergence analysis for each equation has a different structure. Moreover, as an application of this summation formula, we consider the numerical solution of the fractional ordinary differential equations (FODEs) by transforming FODEs into the associated weakly singular Volterra integral equations of the first kind. Some numerical illustrations are designed to depict the accuracy and versatility of the idea.

SOLUTION TO THE MODEL PROBLEM OF EXCITATION OF LOADED CONIC SLOT ANTENNA BY METHOD OF SINGULAR INTEGRAL EQUATIONS

2016 ◽  
Vol 75 (20) ◽  
pp. 1799-1812
Author(s):  
V. A. Doroshenko ◽  
S.N. Ievleva ◽  
N.P. Klimova ◽  
A. S. Nechiporenko ◽  
A. A. Strelnitsky
Keyword(s):  
Integral Equations ◽  
Singular Integral ◽  
Model Problem ◽  
Singular Integral Equations ◽  
Slot Antenna

Singular integral equations in the bound-state problem

1965 ◽  
Vol 35 (3) ◽  
pp. 913-932 ◽  
Author(s):  
G. Cosenza ◽  
L. Sertorio ◽  
M. Toller
Keyword(s):  
Integral Equations ◽  
Singular Integral ◽  
Singular Integral Equations ◽  
Bound State ◽  
State Problem ◽  
Bound State Problem
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