In this article, the second kind Chebyshev wavelet method is presented for solving a class of multi-order fractional differential equations (FDEs) with variable coefficients. We first construct the second kind Chebyshev wavelet, prove its convergence and then derive the operational matrix of fractional integration of the second kind Chebyshev wavelet. The operational matrix of fractional integr...

We present in this paper several extremely efficient and accurate spectral-Galerkin methods for secondand fourth-order equations in polar and cylindrical geometries. These methods are based on appropriate variational formulations which incorporate naturally the pole condition(s). In particular, the computational complexities of the Chebyshev–Galerkin method in a disk and the Chebyshev–Legendre–...

ON HERMITE-FEJER TYPE INTERPOLATION ON THE CHEBYSHEV NODES GRAEME J. BYRNE, T.M. MILLS AND SIMON J. SMITH Given / £ C[-l, 1], let Hn,3(f,x) denote the (0,1,2) Hermite-Fejer interpolation polynomial of / based on the Chebyshev nodes. In this paper we develop a precise estimate for the magnitude of the approximation error |£Tn,s(/,x) — f(x)\. Further, we demonstrate a method of combining the dive...

The recently proposed Chebyshev-like lifting map for the zeros of a uni-variate polynomial was motivated by its applications to splitting a univariate polynomial p(x) numerically into factors, which is a major step of some most eeective algorithms for approximating polynomial zeros. We complement the Chebyshev-like lifting process by a descending process, decrease the estimated computational co...

A limited diffraction beams ~LDB! imaging system with Chebyshev weighting is presented. The objective of the paper is to reduce the sidelobes of the LDB without impacting on main-lobe performance and increase the contrast-resolution of the imaging system. The Chebyshev weighting is applied to the LDB and an analytic description and the simulation results are obtained. Theoretical analysis and s...

Abstract: In this paper, a numerical method to solve nonlinear Fredholm integral equations of second kind is proposed and some numerical notes about this method are addressed. The method utilizes Chebyshev wavelets constructed on the unit interval as a basis in the Galerkin method. This approach reduces this type of integral equation to solve a nonlinear system of algebraic equation. The method...

Algebraic properties of Chebyshev polynomials are presented. The complete factorization of Chebyshev polynomials of the rst kind (Tn(x)) and second kind (Un(x)) over the integers are linked directly to divisors of n and n + 1 respectively. For any odd integer n, it is shown that the polynomial Tn(x)=x is irreducible over the integers i n is prime. The result leads to a generalization of Fermat'...

We give an alternative proof to the well known fact that each convex compact centrally symmetric subset of R2 containing the origin is a zonoid, i.e., the range of a two dimensional vector measure, and we prove that a two dimensional zonoid whose boundary contains the origin is strictly convex if and only if it is the range of a Chebyshev measure. We give a condition under which a two dimension...

We analyze the Legendre and Chebyshev spectral Galerkin semidiscretizations of a one dimensional homogeneous parabolic problem with nonconstant coefficients. We present error estimates for both smooth and nonsmooth data. In the Chebyshev case a limit in the order of approximation is established. On the contrary, in the Legendre case we find an arbitrary high order of convegence.

Through a geometncal approach of the blossoming pnnciple, we achieve a dimension élévation process for extended Chebyshev spaces Applied to a nested séquence ofsuch spaces included in a polynomial one, this allows to compute the Bézier points from the initial Chebyshev-Bézier points This method leads to interesting shape effects © Elsevier, Paris