In this paper, the Chebyshev-I conformable differential equation is considered. A proper power series examined; there are two solutions, even solution and odd solution. The Rodrigues’ type formula also allocated for polynomials.

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...

The main aim of this paper is to discuss about, Chebyshev wavelets based approximation solution for linear and non-linear differential equations arising in science and engineering. The basic idea of this method is to obtain the approximate solution of a differential equation in a series of Cheybyshev wavelets. For this purpose, operational matrix for Cheybyshev wavelets is derived. By applying ...

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 ...

the main purpose of this paper is to propose a new numerical method for solving the optimal control problems based on state parameterization. here, the boundary conditions and the performance index are first converted into an algebraic equation or in other words into an optimization problem. in this case, state variables will be approximated by a new hybrid technique based on new second kind ch...

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.

In the present paper polynomial interpolating scaling function and wavelets are constructed by using the interpolation properties of de la Vallée Poussin kernels with respect to the four kinds of Chebyshev weights. For the decomposition and reconstruction of a given function efficient algorithms based on fast discrete cosine and sine transforms are proposed.

In this paper, we propose a new method to design an observer and control the linear singular systems described by Chebyshev wavelets. The idea of the proposed approach is based on solving the generalized Sylvester equations. An example is also given to illustrate the procedure.