An efficient automatic quadrature procedure is developed for numerically computing the integrals 0 , where the function is smooth and nonoscillatory at infinity and is the Bessel functions of order ν =1,0 and 1/4. The procedure involves the use of an automatic integration scheme of modified FFT used for evaluating Fourier integrals and product type integration, and the modified W-transformation...

ÐHighly-accurate solutions for the lid-driven cavity ̄ow are computed by a Chebyshev collocation method. Accuracy of the solution is achieved by using a substraction method of the leading terms of the asymptotic expansion of the solution of the Navier±Stokes equations in the vicinity of the corners, where the velocity is discontinuous. Critical comparison with former numerical experiments con®r...

The Fitzhugh-Nagumo (fn) mathematical model characterizes the action potential of the membrane. The dynamics of the Fitzhugh-Nagumo model have been extensively studied both with a view to their biological implications and as a test bed for numerical methods, which can be applied to more complex models. This paper deals with the dynamics in the (FH) model. Here, the dynamics are analyzed, qualit...

The range and sparsity of the one-electron density matrix (DM) in Density Functional Theory (DFT) is studied for large systems using the analytical properties of its Chebyshev expansion. General estimates of the range of the DM are derived, showing that the range is inversely proportional to the square-root of an insulator band gap and inversely proportional to the square-root of the temperatur...

A weighted orthogonal system on the half-line based on the Chebyshev rational functions is introduced. Basic results on Chebyshev rational approximations of several orthogonal projections and interpolations are established. To illustrate the potential of the Chebyshev rational spectral method, a model problem is considered both theoretically and numerically: error estimates for the Chebyshev ra...

This paper provides a rigorous and delicate analysis for exponential decay of Jacobi polynomial expansions of analytic functions associated with the Bernstein ellipse. Using an argument that can recover the best estimate for the Chebyshev expansion, we derive various new and sharp bounds of the expansion coefficients, which are featured with explicit dependence of all related parameters and val...

This paper presents a short survey of convergence results and properties of the Lebesgue function kmn(x) for (0, 1 , . . . , m) Hermite-Fejer interpolation based on the zeros of the nth Chebyshev polynomial of the first kind. The limiting behaviour as n -*• oo of the Lebesgue constant Amn = max{Xm n(x) : — 1 < x < 1} for even m is then studied, and new results are obtained for the asymptotic ex...

In this work, we develop fast algorithms for computations involving finite expansions in Gegenbauer polynomials. We describe a method to convert a linear combination of Gegenbauer polynomials up to degree n into a representation in a different family of Gegenbauer polynomials with generally O(n log(1/ε)) arithmetic operations where ε is a prescribed accuracy. Special cases where source or targe...

The maximum entropy method is a theoretically sound approach to construct an analytical form for the probability density function (pdf) given a sample of random events. In practice, numerical methods employed to determine the appropriate Lagrange multipliers associated with a set of moments are generally unstable in the presence of noise due to limited sampling. A robust method is presented tha...

Odd degree Chebyshev polynomials over a ring of modulo 2 have two kinds of period. One is an “orbital period”. Odd degree Chebyshev polynomials are bijection over the ring. Therefore, when an odd degree Chebyshev polynomial iterate affecting a factor of the ring, we can observe an orbit over the ring. The “ orbital period ” is a period of the orbit. The other is a “degree period”. It is observe...