Print ISSN: 1681-6900

Online ISSN: 2412-0758

Keywords : Bernstein polynomials

Collocation Orthonormal Bernstein Polynomials Method for Solving Integral Equations

Suha. N. Shihab; Asmaa. A. A; Mayada.N.Mohammed Ali

Engineering and Technology Journal, 2015, Volume 33, Issue 8, Pages 1493-1502

In this paper, we use a combination of Orthonormal Bernstein functions on the interval [0,1] for degree m=5,and 6 to produce anew approach implementing Bernstein operational matrix of derivative as a method for the numerical solution of linear Fredholm integral equations and Volterra integral equations of the second kind. The method converges rapidly to the exact solution and gives very accurate results even by low value of m. Illustrative examples are included to demonstrate the validity and efficiency of the technique and convergence of the method to the exact solution.

Approximate Solution of Fractional Integro-Differential Equations by Using Bernstein Polynomials

Osama H. Mohammed; Sarmad A. Altaie

Engineering and Technology Journal, 2012, Volume 30, Issue 8, Pages 1362-1373

In this paper, Bernstein piecewise polynomial is used to approximate the
solution of the fractional integro-differential equations, in which the fractional
derivative is described in the (Caputo) sense. Examples are considered to verify the
effectiveness of the proposed derivation, and the approximate solutions guarantee
the desired accuracy.