Browsing by Author "Simos, T.E."
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Item On the fourth order of accuracy difference scheme for the Bitsadze-Samarskii type nonlocal boundary value problem(American Institute of Physics, 2011) Ashyralyev, Allaberen; Simos, T.E.; Öztürk, Elif; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü.; 54403582400The Bitsadze-Samarskii type nonlocal boundary value problem { -d(2)u(t)/dt(2) + Au(t) = f(t), 0 < t < 1, u(0) = phi, u(1) = Sigma(J)(j=1) alpha(j)u(lambda(j)) + psi, (1) Sigma(J)(j=1)vertical bar alpha(j)vertical bar <= 1, 0 < lambda(1) < lambda(2) < ... < lambda(J) < 1 for the differential equation in a Hilbert space H with the self -adjoint positive definite operator A is considered. The fourth order of accuracy difference scheme for approximate solution of the problem is presented. The well posedness of this difference scheme in difference analogue of Holder spaces is established.Item Properties of n-th degree Bernstein polynomials(Amer Inst Pyhsics, 2011) Simos, T.E.; Çetin, Elif; Özbay, Hatice; Togan, Müge; Cangül, İsmail Naci; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Anabilim Dalı.; 0000-0002-0700-5774; 0000-0002-0700-5774; ABA-6206-2020; J-3505-2017; 54402262100; 54403676000; 54403978300; 57189022403In this paper, derivatives of the product of Bernstein polynomials of the same and different degrees are obtained. Also a recurrence formula for those polynomials together with some new properties are given.