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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)

Keywords: Petrov–Galerkin method Jacobi collocation method Jacobi polynomials Jacobi–Gauss–Lobatto quadrature Fast Fourier transform Jacobi–Jacobi Galerkin method a b s t r a c t This paper analyzes a method for solving the third-and fifth-order differential equations with constant coefficients using a Jacobi dual-Petrov–Galerkin method, which is more… (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)