[HTML][HTML] A meshless discrete Galerkin (MDG) method for the numerical solution of integral equations with logarithmic kernels

P Assari, H Adibi, M Dehghan - Journal of computational and applied …, 2014 - Elsevier
This paper describes a computational method for solving Fredholm integral equations of the
second kind with logarithmic kernels. The method is based on the discrete Galerkin method …

A meshless method for the numerical solution of nonlinear weakly singular integral equations using radial basis functions

P Assari, M Dehghan - The European Physical Journal Plus, 2017 - Springer
In this paper a simple and effective method is given for the numerical solution of nonlinear
one-and two-dimensional Fredholm integral equations of the second kind with weakly …

The economized monic Chebyshev polynomials for solving weakly singular Fredholm integral equations of the first kind

ES Shoukralla, MA Markos - Asian-European Journal of …, 2020 - World Scientific
This paper presents a numerical method for solving a certain class of Fredholm integral
equations of the first kind, whose unknown function is singular at the end-points of the …

A new computational method for solving weakly singular Fredholm integral equations of the first kind

ES Shoukralla, M Kamel… - 2018 13th International …, 2018 - ieeexplore.ieee.org
A new computational technique is given for the numerical solution of Fredholm integral
equation of the first kind with a singular density function and a weakly singular logarithmic …

A numerical scheme for solving a class of logarithmic integral equations arisen from two-dimensional Helmholtz equations using local thin plate splines

P Assari, F Asadi-Mehregan, S Cuomo - Applied Mathematics and …, 2019 - Elsevier
This paper presents a numerical method for solving logarithmic Fredholm integral equations
which occur as a reformulation of two-dimensional Helmholtz equations over the unit circle …

[PDF][PDF] Numerical solution of a certain class of singular Fredholm integral equations of the first kind via the Vandermonde matrix

ES Shoukralla, MA Markos - Int J Math Models Methods Appl Sci, 2020 - researchgate.net
In this paper, a computational method is presented to solve potential-type Fredholm integral
equations of the first kind, equations in which the unknown functions are singular at the …

Thin plate spline Galerkin scheme for numerically solving nonlinear weakly singular Fredholm integral equations

P Assari - Applicable Analysis, 2019 - Taylor & Francis
The present work proposes a numerical method to obtain an approximate solution of non-
linear weakly singular Fredholm integral equations. The discrete Galerkin method in …

Mechanical quadrature methods and their splitting extrapolations for boundary integral equations of first kind on open arcs

J Huang, T Lü, ZC Li - Applied numerical mathematics, 2009 - Elsevier
This paper presents the mechanical quadrature methods (MQMs) for solving boundary
integral equations (BIEs) of the first kind on open arcs. The spectral condition number of …

[HTML][HTML] Solving weakly singular integral equations utilizing the meshless local discrete collocation technique

P Assari - Alexandria engineering journal, 2018 - Elsevier
The current work presents a computational scheme to solve weakly singular integral
equations of the second kind. The discrete collocation method in addition to the moving least …

A new Laguerre wavelets‐based method for solving Fredholm integral equations with weakly singular logarithmic kernel

S Behera, SS Ray - Mathematical Methods in the Applied …, 2025 - Wiley Online Library
In this study, a wavelet‐based collocation scheme has been introduced for solving the linear
and nonlinear Fredholm integral equations as well as the system of linear Fredholm integral …