A coupled pair of harmonic equations is solved by the application of Chebyshev acceleration to the Jacobi, Gauss-Seidel, and related iterative methods, where the Jacobi iteration matrix has purely imaginary (or zero) eigenvalues. Comparison is made with a block SOR method used to solve the same problem. Introduction. In [4], we proposed a general block SOR method for solving the biharmonic equa...

In this paper, analysis of linear and nonlinear buckling of relatively thick orthotropic graphene sheets is carried out under mechanical load based on elasticity theories. With the help of  nonlocal elasticity theory, the principle of virtual work, first order shear theory and Von-Karman nonlinear strain, the dominant relationship in terms of obtained displacements has been obtained, and the me...

a method for error estimation of isogeometric analysis of plane stress problems which is the based on stress recovery and using the super convergent properties of the gauss points, has been already introduced. this paper is devoted to the development of the method and study of the effects of these supercovergent points on the solution improvement and error estimation of axisymmetric problems by...

A stochastic version of a stationary linear iterative solver may be designed to converge in distribution to a probability distribution with a specified mean μ and covariance matrix A−1. A common example is Gibbs sampling applied to a multivariate Gaussian distribution which is a stochastic version of the Gauss-Seidel linear solver. The iteration operator that acts on the error in mean and covar...

Nodal point sets, and associated collocation projections, play an important role in a range of high-order methods, including Flux Reconstruction (FR) schemes. Historically, efforts have focused on identifying nodal sets that aim to minimise the L∞ error interpolating polynomial. The present work combines comprehensive review known approximation theory results, with new numerical experiments, mo...

This paper develops a family of preconditioners for pseudospectral approximations of pth-order linear differential operators subject to various types of boundary conditions. The approximations are based on ultraspherical polynomials with special attention being paid to Legendre and Chebyshev polynomial methods based on Gauss–Lobatto quadrature points. The eigenvalue spectrum of the precondition...

8 In his paper " Lagrange interpolation on Chebyshev points of two variables " (J. 9 220–238), Y. Xu proposed a set of Chebyshev like points for polynomial interpolation in the square 10 [−1, 1] 2 , and derived a compact form of the corresponding Lagrange interpolation formula. We inves-11 tigate computational aspects of the Xu polynomial interpolation formula like numerical stability and 12 ef...