Chebyshev Wavelets of the third kind are proposed in this study to solve nonlinear systems FDEs. The main goal method is convert FDE into a system algebraic equations that can be easily solved using matrix methods. In order achieve this, we first generate operational matrices for fractional integration and block-pulse functions (BPF) function approximation. Since obtained sparse, numerical fast...

A conjecture for the projection norm (or Lebesgue constant) of a weighted interpolation method based on the zeros of Chebyshev polynomials of the third and fourth kinds is resolved. This conjecture was made in a paper by J. C. Mason and G. H. Elliott in 1995. The proof of the conjecture is achieved by relating the projection norm to that of a weighted interpolation method based on zeros of Cheb...

Abstract Two efficient quadrature formulae have been developed for evaluating numerically certain singular integral equations of the first kind over the finite interval [-1,1]. Central to this work is the application of four special cases of the Jacobi polynomials P n (x), whose zeros served as interpolation and collocation nodes: (i) α = β = −2 , Tn(x), the first kind Chebyshev polynomials (ii...

In this paper, we will derive the explicit formulae for Chebyshev polynomials of third and fourth kind with odd even indices using combinatorial method. Similar results are also deduced their r-th derivatives. Finally, some identities involving Fibonacci negative obtained.

The properties of two families of s-orthogonal polynomials, which are connected with Chebyshev polynomials of third and fourth kind, are studied. Evaluations of the remainders are given and asymptotic formulae are calculated for the corresponding hyper-Gaussian formulae used for an approximate estimation of integrals. 2000 Mathematics Subject Classification: 33C45, 65D32.

This paper presents a general approach to a multiresolution analysis and wavelet spaces on the interval Our method is based on the Chebyshev transform correspond ing shifts and the discrete cosine transform DCT For the wavelet analysis of given functions e cient decomposition and reconstruction algorithms are proposed using fast DCT algorithms As examples for scaling functions and wavelets poly...

In this paper, a numerical method is proposed to solve FredholmVolterra fractional integro-differential equation with nonlocal boundary conditions. For this purpose, the Chebyshev wavelets of second kind are used in collocation method. It reduces the given fractional integro-differential equation (FIDE) with nonlocal boundary conditions in a linear system of equations which one can solve easily...