In this study, a collocation method, one of the type of projection methods based on the generalized Bernstein polynomials, is developed for the solution of high-order linear Fredholm-Volterra integro-differential equations containing derivatives of unknown function in the integral part. The method is valid for the mixed conditions. The convergence analysis and error bounds of the method are also given. Besides, six examples are presented to demonstrate the applicability and validity of the method. ARTICLE HISTORY

A collocation method based on the Bernstein polynomials defined on the interval[a,b]is developed for approximate solutions of the Fredholm-Volterra integrodifferential equation (FVIDE) in the most general form. This method is reduced to linear FVIDE via the collocation points and quasilinearization technique. Some numerical examples are also given to demonstrate the applicability, accuracy, and efficiency of the proposed method.

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.

In this study, an alternative numerical method having regard to the Bernstein operator is generated for approximate solutions of linear differential equations in the most general form under the initial and boundary conditions. Some applications are also revealed to show how the procedure can be performed for the problems.

In this study, a collocation method based on the generalized Bernstein polynomials is derivated for solving nonlinear Fredholm-Volterra integral equations (FVIEs) in the most general form via the quasilinearization technique. Moreover, quadratic convergence and error estimate of the proposed method is analyzed. Some examples are also presented to show the accuracy and applicability of the method.