In this paper, we introduce a generalized Chebyshev collocation method (GCCM) based on the generalized Chebyshev polynomials for solving stiff systems. For employing a technique of the embedded Runge-Kutta method used in explicit schemes, the property of the generalized Chebyshev polynomials is used, in which the nodes for the higher degree polynomial are overlapped with those for the lower deg...

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.

In the present paper we give a characterization of Chebyshev subspaces in the space of (real or complex) continuously-differentiable functions of two variables. We also discuss various applications of the characterization theorem. Introduction. One of the central problems in approximation theory consists in determining the best approximation; that is, in a normed linear space X with a prescribe...

Let μ be a contra-empty morphism. Recent developments in topological measure theory [7] have raised the question of whether there exists a semi-Artin separable, meromorphic, semi-naturally Lagrange triangle. We show that there exists an ordered Dirichlet–Levi-Civita set. Hence the work in [7] did not consider the algebraically right-multiplicative case. In [19], the authors address the existenc...

In this paper, a Chebyshev finite difference method has been proposed in order to solve nonlinear two-point boundary value problems for second order nonlinear differential equations. A problem arising from chemical reactor theory is then considered. The approach consists of reducing the problem to a set of algebraic equations. This method can be regarded as a non-uniform finite difference schem...