Gegenbauer Series for Numerical Solution of Fredholm Integral Equations of the Second Kind

In this work, to solve the integral equation we rely on the technique of orthogonal polynomials, as some authors have shown in the past [11,12]. However, this work, which simplifies the integral equation in the form of a matrix where it corresponds to a set of linear algebraic equations. Here we rely on the approximation of a series called the Gegenbauer series, which leads us to a rough and effective solution where the error obtained is small compared to the results obtained by some authors.