In Euclidean spaces, the geometric notions of nearest-points map, farthestpoints map, Chebyshev set, Klee set, and Chebyshev center are well known and well understood. Since early works going back to the 1930s, tremendous theoretical progress has been made, mostly by extending classical results from Euclidean space to Banach space settings. In all these results, the distance between points is i...

The problem of natural convection about a cone embedded in a porous medium at local Rayleigh numbers based on the boundary layer approximation and the Darcy’s law have been studied before. Similarity solutions for a full cone with the prescribed wall temperature or surface heat flux boundary conditions which is the power function of distance from the vertex of the inverted cone give us a third-...

In this paper, a super spectral viscosity method using the Chebyshev differential operator of high order Ds = ( √ 1− x2∂x) is developed for nonlinear conservation laws. The boundary conditions are treated by a penalty method. Compared with the second-order spectral viscosity method, the super one is much weaker while still guaranteeing the convergence of the bounded solution of the Chebyshev–Ga...

The usual way to determine the asymptotic behavior of the Chebyshev coefficients for a function is to apply the method of steepest descent to the integral representation of the coefficients. However, the procedure is usually laborious. We prove an asymptotic upper bound on the Chebyshev coefficients for the kth integral of a function. The tightness of this upper bound is then analyzed for the c...

1. Introduction and Summary. Clenshaw [1, 2] has described a simple and effective method for summing a Chebyshev series based on the recurrence relation between the Chebyshev coefficients. He has further pointed out that the same method could be used to sum a series of any set of functions which are generated by a linear recurrence relation [1]. Such a set of functions is a set of orthogonal po...

In this paper, the Chebyshev spectral collocation method(CSCM) for one-dimensional linear hyperbolic telegraph equation is presented. Chebyshev spectral collocation method have become very useful in providing highly accurate solutions to partial differential equations. A straightforward implementation of these methods involves the use of spectral differentiation matrices. Firstly, we transform ...

In a recent article, the first and second kinds of multivariate Chebyshev polynomials fractional degree, relevant integral repesentations, have been studied. this we introduce pseudo-Lucas functions show possible applications these new functions. For kind, compute Newton sum rules any orthogonal polynomial set starting from entries Jacobi matrix. representation formulas for powers r×r matrix, a...

A numerical method for Riccati equation is presented in this work. The method is based on the replacement of unknown functions through a truncated series of hybrid of block-pulse functions and Chebyshev polynomials. The operational matrices of derivative and product of hybrid functions are presented. These matrices together with the tau method are then utilized to transform the differential equ...