A new operational matrix of derivative for orthonormal bernstein polynomial's

Abstract EN

In this paper, an orthonormal family has been constracted {b i6}i 6= 0 of polynomials of degree six is first constructed by using Gram-Schmidt orthonormalization process on Bernstein polynomials {b i6}i 6= 0.

Then, an orthonormal Bernstein operational matrix of derivative Db is derived.Finally, the orthonormal Bernstein expansions along with operational matrix of derivative are applied for variational problemsapproximately.