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...

This paper analyses a Chebyshev pseudospectral collocation semidiscrete (continuous in time) discretization of a variable coefficient parabolic problem. Optimal stability and convergence estimates are given. The analysis is based on an approximation property concerning the GaussLobatto-Chebyshev interpolation operator.

Gordon G Johnson* ([email protected]), Department of Mathematics, University of Houston, Houston, TX 77204-3008. The Closure in a Hilbert Space of a PreHilbert Space CHEBYSHEV Set Fails to be a CHEBYSHEV Set. Preliminary report. E is the real inner product space that is union of all finite-dimensional Euclidean spaces, S is a certain bounded nonconvex set in the E having the property that every...

Poisson equation is frequently encountered in mathematical modeling for scientific and engineering applications. Fast Poisson numerical solvers for 2D and 3D problems are, thus, highly requested. In this paper, we consider solving the Poisson equation ∇2u = f(x, y) in the Cartesian domain Ω = [−1, 1] × [−1, 1], subject to all types of boundary conditions, discretized with the Chebyshev pseudosp...

 Abstract: There are some methods for solving integro-differential equations. In this work, we solve the general-order Feredholm integro-differential equations. The Petrov-Galerkin method by considering Chebyshev multiwavelet basis is used. By using the orthonormality property of basis elements in discretizing the equation, we can reduce an equation to a linear system with small dimension. For ...