In this article a modification of the Chebyshev collocation method is applied to the solution of space fractional differential equations.The fractional derivative is considered in the Caputo sense.The finite difference scheme and Chebyshev collocation method are used .The numerical results obtained by this way have been compared with other methods.The results show the reliability and efficiency...

1. R. L. Adler & T. J. Rivlin. "Ergodic and Mixing Properties of Chebyshev Polynomials." Proa. Amer. Math. Soc. 15 (1964) :79'4-7'96. 2. P. Johnson & A. Sklar. "Recurrence and Dispersion under Iteration of Cebysev Polynomials." To appear. 3. C.H. Kimberling. "Four Composition Identities for Chebyshev Polynomials." This issue, pp. 353-369. 4. T. J. Rivlin. The Chebyshev Polynomials. New York: Wi...

We analyze the asymptotic rates of convergence of Chebyshev, Legendre and Jacobi polynomials. One complication is that there are many reasonable measures of optimality as enumerated here. Another is that there are at least three exceptions to the general principle that Chebyshev polynomials give the fastest rate of convergence from the larger family of Jacobi polynomials. When f (x) is singular...

The mathematical theory of closed form functions for calculating LSFs on the basis of generating functions is presented. Exploiting recurrence relationships in the series expansion of Chebyshev polynomials of the first kind makes it possible to bootstrap iterative LSF-search from a set of characteristic polynomial zeros. The theoretical analysis is based on decomposition of sequences into symme...

We establish several convexity results which are concerned with nonconvex quadratic matrix (QM) functions: strong duality of quadratic matrix programming problems, convexity of the image of mappings comprised of several QM functions and the existence of a corresponding SLemma. As a consequence of our results, we prove that a class of quadratic problems involving several functions with similar m...

A family of digital parametric audio equalizers based on high-order Butterworth, Chebyshev, and elliptic analog prototype filters is derived that generalizes the conventional biquadratic designs and provides flatter passbands and sharper bandedges. The equalizer filter coefficients are computable in terms of the center frequency, peak gain, bandwidth, and bandwidth gain. We consider the issues ...

It is known that Fairlie–Odesskii algebra U ′ q(so3) appears as algebra of observables in quantum gravity in (2 + 1)-dimensional de Sitter space with space being torus. In this paper, we study the center of this algebra at q a root of 1. It turns out that Casimir elements in this case are algebraically dependent. Using realization of the algebra U ′ q(so3) in terms of quantized lengths of geode...

A superconducting slot antenna combined with a bandpass filter composed of coplanar waveguide meanderline resonators has been designed and tested. Based on a new design theory for broadband impedance matching circuits, we designed a slot antenna with a small radiation resistance of 1 X impedance matched to a three-pole Chebyshev bandpass filter with 10 GHz center frequency and 0.35% fractional ...

In this work, the definition of first and second types multiplicative Chebyshev differential equations is given solutions these are investigated with help power series. Also, properties type polynomials proved. Finally, studies supported numerical examples.

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...