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. Finallysome examples and their numerical solutions are given; comparing the results with the numerical resultsobtained from the other methods, we show the high accuracy and efficiency of the proposed method.
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