A collocation method for linear integral equations in terms of the generalized Bernstein polynomials

Abstract

In this study, a collocation method based on the generalized Bernstein polynomials is presented and analized for the solution of linear Fredholm-Volterra integral equations (FVIEs). Error bounds and convergence of this method are demonstrated. Some examples are also given to illustrate the accuracy, efficiency and applicability of the method.

A Bernstein polynomial approach for solution of nonlinear integral equations

“…Some systematic studies of this property have been given in [1, 5-7, 11, 13-15, 18]. This method is also a powerful tool to obtain the approximate solution of nonlinear problems included such as differential equations [1,3,5,9,14,17], functional differential equations [2,7], integral equations [13,15] and integro-differential equations [4,18].…”