A Numerical Solution of the Urysohn-Type Fredholm İntegral Equations

Abstract

In the present paper, a combination of the Bernstein polynomials and artificial neural networks (ANNs) is presented for solving the non-linear Urysohn equation. These polynomials are utilized to reduce the solution of the given problem to the solution of a system of non-linear algebraic equations. The remaining set of nonlinear equations is solved numerically by using the ANNs approach to yield truncated Bernstein series coefficients of the solution function. Several illustrative examples with numerical simulations are provided to support the theoretical claims.