Some properties of near-Toeplitz tridiagonal matrices with specific perturbations in the first and last main diagonal entries are considered. Applying the relation between the determinant and Chebyshev polynomial of the second kind, we first give the explicit expressions of determinant and characteristic polynomial, then eigenvalues are shown by finding the roots of the characteristic polynomia...

In this paper Chebyshev wavelet and their properties are employed for deriving Chebyshev wavelet operational matrix of fractional derivatives and a general procedure for forming this matrix is introduced. Then Chebyshev wavelet expansion along with this operational matrix are used for numerical solution of Bagley-Torvik boundary value problems. The error analysis and convergence properties of t...

Abstract We develop a diagrammatic categorification of the polynomial ring Z[x], based on geometrically defined graded algebra. This construction generalizes to some special functions, such as Chebyshev polynomials. Diagrammatic algebras featured in these categorifications lead first topological interpretations Bernstein-Gelfand-Gelfand reciprocity property.

We construct an orthogonal wavelet basis for the interval using a linear combination of Legendre polynomials. The coefficients are taken as appropriate roots of Chebyshev polynomials of the second kind. The one-dimensional transform is applied to analytical data and appropriate definitions of a scalogram as well as local and global spectra are presented. The transform is then extended to the mu...

Some properties of near-Toeplitz tridiagonal matrices with specific perturbations in the first and last main diagonal entries are considered. Applying the relation between the determinant and Chebyshev polynomial of the second kind, we first give the explicit expressions of determinant and characteristic polynomial, then eigenvalues are shown by finding the roots of the characteristic polynomia...

In this paper, we will introduce a method to find a numerical solution of nonlinear age-structured population model using second-kind Chebyshev polynomials. This method convert the nonlinear age-structured population models to an equivalent differential equation. We introduce two variable second-kind Chebyshev polynomials and their basic properties. These properties will be used to reduce the o...

We reveal the relationship between a Petrov–Galerkin method and a spectral collocation method at the Chebyshev points of the second kind (±1 and zeros of Uk) for the two-point boundary value problem. Derivative superconvergence points are identified as the Chebyshev points of the first kind (Zeros of Tk). Super-geometric convergent rate is established for a special class of solutions.

The Chebyshev polynomials have many beautiful properties and countless applications, arising in a variety of continuous settings. They are a sequence of orthogonal polynomials appearing in approximation theory, numerical integration, and differential equations. In this paper we approach them instead as discrete objects, counting the sum of weighted tilings. Using this combinatorial approach, on...