An Analytical Solution to the Non-linear Fredholm Integral Equation of the Second Kind using a Polynomial Expansion Scheme

The aim of this paper is to provide an analytical solution to the non-linear Fredholm integral equation inside a symmetrical physical model. For this propose, a polynomial expansion method is proposed. The studied physical model is based on the concept of two circular coaxial conducting disks, separated by a fixed distance and held at equal or opposite potentials. The performed protocol is based on the Boubaker Polynomials Expansion Scheme (BPES). The asymptotic behaviors of the potential field created conjointly by the coaxial disks are also highlighted in comparison with some recently recorded results.