On the Derivatives of Bernstein Polynomials: An Application for the Solution of High Even-Order Differential Equations
نویسندگان
چکیده
A new formula expressing explicitly the derivatives of Bernstein polynomials of any degree and for any order in terms of Bernstein polynomials themselves is proved, and a formula expressing the Bernstein coefficients of the general-order derivative of a differentiable function in terms of its Bernstein coefficients is deduced. An application of how to use Bernstein polynomials for solving high even-order differential equations by Bernstein Galerkin and Bernstein PetrovGalerkin methods is described. These two methods are then tested on examples and compared with other methods. It is shown that the presented methods yield better results.
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