In the paper, the authors establish two identities to express higher order derivatives and integer powers of the generating function of the Chebyshev polynomials of the second kind in terms of integer powers and higher order derivatives of the generating function of the Chebyshev polynomials of the second kind respectively, find an explicit formula and an identity for the Chebyshev polynomials ...

In this paper, a Chebyshev–Legendre spectral viscosity (CLSV) method is developed for nonlinear conservation laws with initial and boundary conditions. The boundary conditions are dealt with by a penalty method. The viscosity is put only on the high modes, so accuracy may be recovered by postprocessing the CLSV approximation. It is proved that the bounded solution of the CLSV method converges t...

A novel Gaussian state estimator named Chebyshev Polynomial Kalman Filter is proposed that exploits the exact and closed-form calculation of posterior moments for polynomial nonlinearities. An arbitrary nonlinear system is at first approximated via a Chebyshev polynomial series. By exploiting special properties of the Chebyshev polynomials, exact expressions for mean and variance are then provi...

In this paper we will present an approach to realize FIR filters using Chebyshev Polynomials. Chebyshev polynomials play a vital role in antenna as well as in signal processing theory. The FIR filter design has also been disscussed previously [2-10], these papers discuss approximation methods, while the approach we will discuss in this paper gives exact design of FIR filter in Chebyshev sense. ...

This paper analyses a Chebyshev pseudospectral collocation semidiscrete (continuous in time) discretization of a variable coefficient parabolic problem. Optimal stability and convergence estimates are given. The analysis is based on an approximation property concerning the GaussLobatto-Chebyshev interpolation operator.

The control approach for chaotic systems is one of the hottest research topics in nonlinear area. This paper is concerned with the controller design problem for chaotic systems. The particle swarm optimization (PSO) algorithm is firstly proposed to search for the weights of the Chebyshev neural networks (CNNs), and then an adaptive controller for the chaotic systems is designed based on the PSO...

A bivariate Chebyshev polynomials approach is proposed to estimate the dynamic response bounds of nonlinear systems with interval uncertainties. The existing collocation method directly searches maximum and minimum values surrogate model in entire space by scanning (SM). presence too many uncertain parameters will lead expansive computational cost. To overcome this shortcoming, decomposed a fun...

Compared to Krylov space methods based on orthogonal or oblique projection, the Chebyshev iteration does not require inner products and is therefore particularly suited for massively parallel computers with high communication cost. Here, six different algorithms that implement this method are presented and compared with respect to roundoff effects, in particular, the ultimately achievable accur...