<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">CHEBBAH, Hasna</style></author><author><style face="normal" font="default" size="100%">MENNOUNI, ABDELAZIZ</style></author><author><style face="normal" font="default" size="100%">Ramdani, Nedjem-Eddine</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Numerical Solution of Generalized Logarithmic Integral Equations of the Second Kind by Projections</style></title><secondary-title><style face="normal" font="default" size="100%">Malaysian Journal of Mathematical SciencesMalaysian Journal of Mathematical Sciences</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2018</style></year><pub-dates><date><style  face="normal" font="default" size="100%">2018</style></date></pub-dates></dates><number><style face="normal" font="default" size="100%">3</style></number><volume><style face="normal" font="default" size="100%">12</style></volume><pages><style face="normal" font="default" size="100%">349–367</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">In this work, we present a new techniques to solve the integral equations of the second kind with logarithmic kernel. First, we show the existence and uniqueness of the solution for the given problem in a Hilbert space. Next, we discuss a projection method for solving integral equations with logarithmic kernel of the second kind; the present method based on the shifted Legendre polynomials. We examine the existence of the solution for the approximate equation, and we provide a new error estimate for the numerical solutions. At the end, numerical examples are provided to illustrate the theoretical results.</style></abstract></record></records></xml>