Comparisons Between Bernstein Polynomials and Homotopy Perturbation Method to Numerical Solutions of Fredholm Integral Equations

Comparisons Between Bernstein Polynomials and Homotopy Perturbation Method to Numerical Solutions of Fredholm Integral Equations

In this paper, Bernstein piecewise polynomials and homotopy perturbation method are used to solve the Fredholm integral equations numerically. A matrix formulation is given for a non-singular linear Fredholm Integral Equation by the technique of Galerkin method. In the Galerkin method, the Bernstein polynomials are exploited as the linear combination in the approximations as basis functions. The homotopy perturbation method is a efficient method for solving a broad spectrum of problems. For use the homotopy perturbation method, a suitable construction of a homotopy equation is of vital importance.