`ISRN Applied MathematicsVolume 2011, Article ID 787694, 15 pageshttp://dx.doi.org/10.5402/2011/787694`
Research Article

## Approximate Solutions of Differential Equations by Using the Bernstein Polynomials

Department of Mathematics, Alzahra University, Tehran, Iran

Received 12 March 2011; Accepted 19 April 2011

Academic Editors: F. Ding and G. Psihoyios

Copyright © 2011 Y. Ordokhani and S. Davaei far. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

A numerical method for solving differential equations by approximating the solution in the Bernstein polynomial basis is proposed. At first, we demonstrate the relation between the Bernstein and Legendre polynomials. By using this relation, we derive the operational matrices of integration and product of the Bernstein polynomials. Then, we employ them for solving differential equations. The method converts the differential equation to a system of linear algebraic equations. Finally some examples and their numerical solutions are given; comparing the results with the numerical results obtained from the other methods, we show the high accuracy and efficiency of the proposed method.