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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… (More)

Keywords: Bernstein polynomials Spectral method High order differential equations a b s t r a c t A new explicit formula for the integrals of Bernstein polynomials of any degree for any order in terms of Bernstein polynomials themselves is derived. A fast and accurate algorithm is developed for the solution of high even-order boundary value problems (BVPs)… (More)

In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: a b s t r a c t We are concerned with linear and nonlinear multi-term fractional… (More)

a r t i c l e i n f o a b s t r a c t Available online xxxx Keywords: Fractional diffusion-wave equations Tau method Shifted Jacobi polynomials Operational matrix Caputo derivative In this paper, an efficient and accurate spectral numerical method is presented for solving second-, fourth-order fractional diffusion-wave equations and fractional wave… (More)

It is well known that spectral methods (tau, Galerkin, collocation) have a condition number of O.N 4 / where N is the number of retained modes of polynomial approximations. This paper presents some efficient spectral algorithms, which have a condition number of O.N 2 /, based on the ultraspherical-Galerkin methods for the integrated forms of second-order… (More)