In this study a numerical method is developed to solve the Hammerstein integral equations. To this end the kernel has been approximated using the leastsquares approximation schemes based on Legender-Bernstein basis. The Legender polynomials are orthogonal and these properties improve the accuracy of the approximations. Also the nonlinear unknown function has been approximated by using the Berns...

in this study a numerical method is developed to solve the hammerstein integral equations. to this end the kernel has been approximated using the leastsquares approximation schemes based on legender-bernstein basis. the legender polynomials are orthogonal and these properties improve the accuracy of the approximations. also the nonlinear unknown function has been approximated by using the berns...

In this paper, we apply spectral method based on the Bernstein polynomials for solving a class of optimal control problems with Jumarie’s modified Riemann-Liouville fractional derivative. In the first step, we introduce the dual basis and operational matrix of product based on the Bernstein basis. Then, we get the Bernstein operational matrix for the Jumarie’s modified Riemann-Liouville fractio...

Abstract — In this paper we derive the matrix of transformation of the Jacobi polynomial basis form into the Bernstein polynomial basis of the same degree n and vice versa. This enables us to combine the superior least-squares performance of the Jacobi polynomials with the geometrical insight of the Bernstein form. Application to the inversion of the Bézier curves is given. 2000 Mathematics Sub...

The generalized Bernstein basis in the space Πn of polynomials of degree at most n, being an extension of the q-Bernstein basis introduced recently by G.M. Phillips, is given by the formula (see S. Lewanowicz & P. Woźny, BIT 44 (2004), 63–78) Bn i (x;ω| q) := 1 (ω; q)n [ n i ] q x (ωx−1; q)i (x; q)n−i (i = 0, 1, . . . , n). We give explicitly the dual basis functions Dn k (x; a, b, ω| q) for th...

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 paper [4], transformation matrices mapping the Legendre and Bernstein forms of a polynomial of degree n into each other are derived and examined. In this paper, we derive a matrix of transformation of Chebyshev polynomials of the first kind into Bernstein polynomials and vice versa. We also study the stability of these linear maps and show that the Chebyshev–Bernstein basis conversion is rem...