A generalised Chebychev functional involving integral means of functions over different intervals is investigated. Bounds are obtained for which the functions are assumed to be of Hölder type. A weighted generalised Chebychev functional is also introduced and bounds are obtained in terms of weighted Grüss, Chebychev and Lupaş inequalities.

We propose and analyze a spectral Jacobi-collocation approximation for fractional order integro-differential equations of FredholmVolterra type. The fractional derivative is described in the Caputo sense. We provide a rigorous error analysis for the collection method, which shows that the errors of the approximate solution decay exponentially in L∞ norm and weighted L2-norm. The numerical examp...

A Legendre spectral collocation method is presented for the solution of the biharmonic Dirichlet problem on a square. The solution and its Laplacian are approximated using the set of basis functions suggested by Shen, which are linear combinations of Legendre polynomials. A Schur complement approach is used to reduce the resulting linear system to one involving the approximation of the Laplacia...

In this paper, we propose an iterative spectral method for solving differential equations with initial values on large intervals. In the proposed method, we first extend the Legendre wavelet suitable for large intervals, and then the Legendre-Guass collocation points of the Legendre wavelet are derived. Using this strategy, the iterative spectral method converts the differential equation to a s...

In this study, a spectral collocation domain decomposition method is developed for the numerical solution of second and fourth order problems in circular domains. The method is applied to the Navier-Stokes equations and its performance is investigated in the cases of the stream function and the stream function-vorticity formulations.

This paper gives an efficient numerical method for solving the nonlinear system of Volterra-Fredholm integral equations. A Legendre-spectral method based on the Legendre integration Gauss points and Lagrange interpolation is proposed to convert the nonlinear integral equations to a nonlinear system of equations where the solution leads to the values of unknown functions at collocation points.

We propose a spectral method that discretizes the Boltzmann collision operator and satisfies a discrete version of the H-theorem. The method is obtained by modifying the existing Fourier spectral method to match a classical form of the discrete velocity method. It preserves the positivity of the solution on the Fourier collocation points and as a result satisfies the H-theorem. The fast algorit...

The stability and dynamics of nonlinear Schrödinger superflows past a twodimensional disk are investigated using a specially adapted pseudo-spectral method based on mapped Chebychev polynomials. This efficient numerical method allows the imposition of both Dirichlet and Neumann boundary conditions at the disk border. Small coherence length boundary-layer approximations to stationary solutions a...