We present five theorems concerning the asymptotic convergence rates of Chebyshev interpolation applied to functions transplanted to either a semi-infinite or an infinite interval under exponential or double-exponential transformations. This strategy is useful for approximating and computing with functions that are analytic apart from endpoint singularities. The use of Chebyshev polynomials ins...

q-Analogs of Classical 6-Periodicity: From Euler to Chebyshev Boris A KUPERSHMIDT The University of Tennessee Space Institute, Tullahoma, TN 37388, USA E-mail: [email protected] Received November 19, 2002; Accepted January 03, 2003 Abstract The sequence of period 6 starting with 1, 1, 0,−1,−1, 0 appears in many different disguises in mathematics. Various q-versions of this sequence are found, a...

In solving semilinear initial boundary value problems with prescribed non-periodic boundary conditions using implicit-explicit and implicit time stepping schemes, both the function and derivatives of the function may need to be computed accurately at each time step. To determine the best Chebyshev collocation method to do this, the accuracy of the real space Chebyshev differentiation, spectral ...

In this paper, we study the Chebyshev property of the 3-dimentional vector space $E =langle I_0, I_1, I_2rangle$, where $I_k(h)=int_{H=h}x^ky,dx$ and $H(x,y)=frac{1}{2}y^2+frac{1}{2}(e^{-2x}+1)-e^{-x}$ is a non-algebraic Hamiltonian function. Our main result asserts that $E$ is an extended complete Chebyshev space for $hin(0,frac{1}{2})$. To this end, we use the criterion and tools developed by...

The focus of this paper is on the numerical solution of linear systems of Fredhlom integral equations of the second kind. For this purpose, the Chebyshev cardinal functions with Gauss-Lobatto points are used. By combination of properties of these functions and the effective Clenshaw-Curtis quadrature rule, an applicable numerical method for solving the mentioned systems is formulated. Some erro...

This paper reviews the notion of interpolation of a smooth function by means of Chebyshev polynomials, and the well-known associated results of spectral accuracy when the function is analytic. The rate of decay of the error is proportional to ρ−N , where ρ is a bound on the elliptical radius of the ellipse in which the function has a holomorphic extension. An additional theorem is provided to c...