Numerical Solutions of Fredholm Integral Equations of Second Kind Using Piecewise Bernoulli Polynomials

Abstract

The aim of this paper is to solve the Fredholm integral equations numerically using piecewise Bernoulli polynomials. The modified
Bernoulli polynomials are derived explicitly over the unit interval. A matrix formulation for non-singular linear Fredholm integral
equations is derived by the technique of Galerkin method. In this method, the Bernoulli polynomials are exploited as basis functions in
the approximation. Numerical examples are considered to verify the accuracy of the proposed derivations.