Numerical Method for the Solution of Integro-Differential Equations of the Second Kind

Abstract

The purpose of this work is to search for an approximate solution to the Fredholm and Volterra integro-differential equations using Genocchi polynomials, replacing the initial conditions if necessary, where the integrals can be calculated using numerical methods, in order to obtain a variation problem and reduce it to a linear system, where its solution is to find the coefficients of the function. Unknowns and then solve the equation. The convergence and effectiveness of this method are confirmed by numerical examples that will be presented.