Malaysian Journal of Mathematical Sciences, September 2018, Vol. 12, No. 3
Numerical Solution of Generalized Logarithmic Integral Equations of the Second Kind by Projections
Chebbah, H., Mennouni, A. and Ramdani, N. E.
Corresponding Email: aziz.mennouni@yahoo.fr
Received date: 12 November 2017
Accepted date: 8 September 2018
Abstract:
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.
Keywords: Logarithmic kernel, integral equations, projection approximations, shifted Legendre polynomials
