Numerical solution of a Fredholm integral equation of the second kind involving some dual series equations

Abstract

In this article, the Laplace equation with nonhomogenous mixed boundary conditions, defined on a surface of semi-infinite cylinder is solved by using dual series equations (DSE). The DSE method is based on transforming the mixed problem to a Fredholm integral equation of second kind, where the resulted integral equation is equipped with kernel defined of infinite integral. We solved the equation by using numerical quadrature method and obtain the numerical solution for the Laplace equation.