In this paper, the Ritz-Galerkin method in Bernstein polynomial basis is applied for solving the nonlinear problem of the magnetohydrodynamic (MHD) flow of third grade fluid between the two plates. The properties of the Bernstein  polynomials together with the Ritz-Galerkin method are used to reduce the solution of the MHD Couette flow of non-Newtonian fluid in a porous medium to the solution o...

In the present work, by applying known Bernstein polynomials and their advantageous properties, we establish an efficient iterative algorithm to approximate the numerical solution of fuzzy Fredholm integral equations of the second kind. The convergence of the proposed method is given and the numerical examples illustrate that the proposed iterative algorithm are ‎valid.‎

In this paper, we introduce hybrid of block-pulse functions and Bernstein polynomials and derive operational matrices of integration, dual, differentiation, product and delay of these hybrid functions by a general procedure that can be used for other polynomials or orthogonal functions. Then, we utilize them to solve delay differential equations and time-delay system. The method is based upon e...

The Volterra delay integral equations have numerous applications in various branches of science, including biology, ecology, physics and modeling of engineering and natural sciences. In many cases, it is difficult to obtain analytical solutions of these equations. So, numerical methods as an efficient approximation method for solving Volterra delay integral equations are of interest to many res...

In this paper, the Bernstein polynomials are used to approximate the solutions of linear integral equations with multiple time lags (IEMTL) through expansion methods (collocation method, partition method, Galerkin method). The method is discussed in detail and illustrated by solving some numerical examples. Comparison between the exact and approximated results obtained from these methods is car...

In this paper, we present a new computational method to solve Volterra integral equations of the first kind based on Bernstein polynomials. In this method, using operational matrices turn the integral equation into a system of equations. The computed operational matrices are exact and new. The comparisons show this method is acceptable. Moreover, the stability of the proposed method is studied.

in this paper we present a new method for solving fractional optimal control problems with delays in state and control. this method is based upon bernstein polynomial basis and using feedback control. the main advantage of using feedback or closed-loop controls is that they can monitor their effect on the system and modify the output accordingly. in this work, we use bernstein polynomials to tr...

In this paper operational matrix of Bernstein Polynomials (BPs) is used to solve Bratu equation. This nonlinear equation appears in the particular elecotrospun nanofibers fabrication process framework. Elecotrospun organic nanofibers have been used for a large variety of filtration applications such as in non-woven and filtration industries. By using operational matrix of fractional integration...