scholarly journals Numerical solution of weakly singular Fredholm integral equations via generalization of the Euler–Maclaurin summation formula

2014 ◽  
Vol 8 (2) ◽  
pp. 200-205 ◽  
Author(s):  
Reza Behzadi ◽  
Emran Tohidi ◽  
Faezeh Toutounian
Keyword(s):  
Numerical Solution ◽  
Integral Equations ◽  
Summation Formula ◽  
Fredholm Integral Equations ◽  
Weakly Singular

scholarly journals A note on orthogonal polynomials

1970 ◽  
Vol 17 (1) ◽  
pp. 83-94 ◽  
Author(s):  
D. Kershaw
Keyword(s):  
Orthogonal Polynomials ◽  
Numerical Solution ◽  
Integral Equations ◽  
Fredholm Integral Equations ◽  
Intermediate Result ◽  
Weakly Singular Kernels ◽  
Quadrature Formulae ◽  
Weakly Singular ◽  
Gauss Type ◽  
Singular Kernels

During an investigation into the existence of Gauss-type quadrature formulae for the numerical solution of Fredholm integral equations with weakly singular kernels an intermediate result was found which is of independent interest.

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.

scholarly journals On integral equations with Weakly Singular kernel by using Taylor series and Legendre polynomials

Open Physics ◽  
2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Esmail Babolian ◽  
Danial Hamedzadeh ◽  
Hossein Jafari ◽  
Asghar Arzhang Hajikandi ◽  
Dumitru Baleanu
Keyword(s):  
Numerical Solution ◽  
Integral Equations ◽  
Taylor Series ◽  
Unknown Function ◽  
Legendre Polynomials ◽  
Second Order ◽  
Singular Kernel ◽  
Fredholm Integral Equations ◽  
Weakly Singular Kernel ◽  
Weakly Singular

AbstractThis paper is concerned with the numerical solution for a class of weakly singular Fredholm integral equations of the second kind. The Taylor series of the unknown function, is used to remove the singularity and the truncated Taylor series to second order of k(x, y) about the point (x

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