This paper concerns the iterative solution of the linear system arising from the Chebyshev–collocation approximation of second-order elliptic equations and presents an optimal multigrid preconditioner based on alternating line Gauss–Seidel smoothers for the corresponding stiffness matrix of bilinear finite elements on the Chebyshev–Gauss–Lobatto grid.  2000 IMACS. Published by Elsevier Science...

A numerical approximation of the initial-boundary system of nonlinear hyperbolic equations based on spectral collocation method is presented in this article. A Chebyshev-Gauss-Radau collocation (C-GR-C) method in combination with the implicit RungeKutta scheme are employed to obtain highly accurate approximations to the mentioned problem. The collocation points are the Chebyshev interpolation n...

We extend the Chebyshev-Legendre spectral method to multi-domain case for solving the two-dimensional vorticity equations. The schemes are formulated in Legendre-Galerkinmethod while the nonlinear term is collocated at Chebyshev-Gauss collocation points. We introduce proper basis functions in order that the matrix of algebraic system is sparse. The algorithm can be implemented efficiently and i...

The problem of crack propagation along the interface of two bonded dissimilar orthotropic plates is considered. Using Galilean transformation, the problem is reduced to a quasistatic one. Then, using Fourier transforms and asymptotic analysis, the problem is reduced to a pair of singular integral equations with Cauchy-type singularity. These equations are solved using Gauss-Chebyshev quadrature...

We develop a sparse grid spectral element method using nodal bases on Chebyshev-Gauss-Lobatto points for multi-dimensional elliptic equations. Since the quadratures based on sparse grid points do not have the accuracy of a usual Gauss quadrature, we construct the mass and stiffness matrices using a pseudo-spectral approach, which is exact for problems with constant coefficients and uniformly st...

In this paper, the evaluation of I = ∫ 1 −1 f(x) √ 1−x2 dx is proposed by using the opened and closed Gauss Chebyshev integration rules in the stochastic arithmetic. For this purpose, a theorem is proved to show the accuracy of the Gauss-Chebyshev rules. Then, the CESTAC 1 method and the stochastic arithmetic are used to validate the results and implement the numerical example.

In this paper we study convergence and computation of interpolatory quadrature formulas with respect to a wide variety of weight functions. The main goal is to evaluate accurately a definite integral, whose mass is highly concentrated near some points. The numerical implementation of this approach is based on the calculation of Chebyshev series and some integration formulas which are exact for ...

In this paper, Lagrange interpolation in Chebyshev-Gauss-Lobatto nodes is used to develop a procedure for finding discrete and continuous approximate solutions of a singular boundary value problem. At first, a continuous time optimization problem related to the original singular boundary value problem is proposed. Then, using the Chebyshev- Gauss-Lobatto nodes, we convert the continuous time op...

Abstract The new rational a -polynomials are used to solve the Falkner-Skan equation. These polynomials equipped with an auxiliary parameter. approximated solution equation is obtained by unknown coefficients. To find coefficients and parameter contained in polynomials, collocation method Chebyshev-Gauss points used. numerical examples show efficiency of this method.