We reveal the relationship between a Petrov–Galerkin method and a spectral collocation method at the Chebyshev points of the second kind (±1 and zeros of Uk) for the two-point boundary value problem. Derivative superconvergence points are identified as the Chebyshev points of the first kind (Zeros of Tk). Super-geometric convergent rate is established for a special class of solutions.

We develop and analyze a first-order system least-squares spectral method for the second-order elliptic boundary value problem with variable coefficients. We first analyze the Chebyshev weighted norm least-squares functional defined by the sum of the Lwand H−1 w norm of the residual equations and then we replace the negative norm by the discrete negative norm and analyze the discrete Chebyshev ...

We prove two kinds of Lyapunov type inequalities for pseudo-integrals. One discusses pseudo-integrals where pseudo-operations are given by a monotone and continuous function g. The other one focuses on the pseudo-integrals based on a semiring 0; 1 ½ Š; sup; ð Þ , where the pseudo-multiplication is generated. Some examples are given to illustrate the validity of these inequalities. As a generali...

In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: a r t i c l e i n f o a b s t r a c t In the framework of mapped pseudospectral methods, we use a polynomial-type mapping fu...

We investigate the linear stability of unstably strati ed Poiseuille ow between two horizontal parallel plates under non-Boussinesq conditions. It is shown, that Squire's transformation can be used to reduce the three-dimensional stability problem to an equivalent two-dimensional one. The eigenvalue problem, consisting of the generalized Orr-Sommerfeld equations, is solved numerically using an ...

Article history: Received 1 January 2013 Received in revised form 9 September 2013 Accepted 6 October 2013 Available online 22 October 2013

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–...

In this research paper, an improved Chebyshev-Gauss-Lobatto pseudospectral approximation of nonlinear Burger-Huxley and Fitzhugh- Nagumo equations have been presented. The method employs chebyshev Gauss-Labatto points in time and space to obtain spectral accuracy. The mapping has introduced and transformed the initial-boundary value non-homogeneous problem to homogeneous problem. The main probl...

We describe a fast high-order accurate method for the solution of the heat equation in domains with moving Dirichlet or Neumann boundaries and distributed forces. We assume that the motion of the boundary is prescribed. Our method extends the work of Greengard and Strain [Comm. Pure Appl. Math., XLIII (1990), pp. 949–963]. Our scheme is based on a time-space Chebyshev pseudo-spectral collocatio...

In this paper, we introduce the concept of interval pseudo-homegeneous uninorms. We extend the concept of pseudo-homogeneity of specific functions for interval pseudo-homogeneous functions. It is studied two cases of interval pseudo-homogeneous uninorms, that is, interval pseudo-homogeneous tnorms and interval pseudo-homogeneous t-conorms. It is proved a form of interval pseudo-homogeneous t-no...