نتایج جستجو برای: chebyshev expansion

تعداد نتایج: 145338  

Journal: :international journal of advanced design and manufacturing technology 0
sedigheh shahmirzaee jeshvaghany department of mechanical and aerospace engineering, science and research branch, islamic azad university, tehran, iran farshad pazooki department of mechanical and aerospace engineering, science and research branch, islamic azad university, tehran, iran. alireza basohbat novinzaddeh department of aerospace engineering, k.n.toosi university of technology, tehran, iran

in this study, the problem of determining an optimal trajectory of a nonlinear injection into orbit problem with minimum time was investigated. the method was based on orthogonal polynomial approximation. this method consists of reducing the optimal control problem to a system of algebraic equations by expanding the state and control vector as chebyshev or legendre polynomials with undetermined...

Journal: :international journal of industrial mathematics 0
f. goharee department of mathematics, science and research branch, islamic azad university, tehran,iran e. babolian department of mathematics, science and research branch, islamic azad university, tehran,iran

in this paper a modification of he's variational iteration method (vim) has been employed to solve dung and riccati equations. sometimes, it is not easy or even impossible, to obtain the first few iterations of vim, therefore, we suggest to approximate the integrand by using suitable expansions such as taylor or chebyshev expansions.

Journal: :Electr. Notes Theor. Comput. Sci. 2009
Tsuyako Miyakoda

In this paper, we tried to evaluate the fractional derivatives by using the Chebyshev series expansion. We discuss the indefinite quadrature rule to estimate the fractional derivatives of Riemann-Liouville type.

2014
Fakhrodin Mohammadi

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...

2008
Eric Butcher Brian Mann

This chapter provides a brief literature review together with detailed descriptions of the authors’ work on the stability and control of systems represented by linear time-periodic delay-differential equations using the Chebyshev and temporal finite element analysis (TFEA) techniques. Here, the theory and examples assume that there is a single fixed discrete delay which is equal to the principa...

2014
Paul Dalsgaard Ove Andersen

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...

2015
Nicholas Hale Alex Townsend

An O(N(logN)2/ loglogN) algorithm for computing the discrete Legendre transform and its inverse is described. The algorithm combines a recently developed fast transform for converting between Legendre and Chebyshev coefficients with a Taylor series expansion for Chebyshev polynomials about equallyspaced points in the frequency domain. Both components are based on the FFT, and as an intermediate...

2004
S. Z. Peng J. Pan

A new numerical method, named the acoustical wave propagator method, is introduced to describe the dynamic characteristics of one-dimensional structures with discontinuities. The acoustical wave propagator is derived and implemented by combining Chebyshev polynomial expansion and fast Fourier transformation. Numerical accuracy of the acoustical wave propagator method is examined and compared wi...

Formulae expressing explicitly the coefficients of an expansion of double Jacobi polynomials which has been partially differentiated an arbitrary number of times with respect to its variables in terms of the coefficients of the original expansion are stated and proved. Extension to expansion of triple Jacobi polynomials is given. The results for the special cases of double and triple ultraspher...

2014
Haiyong Wang Daan Huybrechs KU Leuven

The computation of spectral expansion coefficients is an important aspect in the implementation of spectral methods. In this paper, we explore two strategies for computing the coefficients of polynomial expansions of analytic functions, including Chebyshev, Legendre, ultraspherical and Jacobi coefficients, in the complex plane. The first strategy maximizes computational efficiency and results i...

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