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chebyshev-approximation
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Polynomial expansion for extraction of electromagnetic eigenmodes in layered structures
, Article Journal of the Optical Society of America B: Optical Physics ; Volume 20, Issue 12 , 2003 , Pages 2434-2441 ; 07403224 (ISSN) ; Rashidian, B ; Sharif University of Technology
Optical Society of America (OSA)
2003
Abstract
A polynomial expansion approach to the extraction of guided and leaky modes in layered structures including dielectric waveguides and periodic stratified media is proposed. To verify the method we compared the results of analysis of a typical test case with those reported in the literature and found good agreement. Polynomial expansion is a nonharmonic expansion and does not involve harmonic functions or intrinsic modes of homogenous layers. This approach has the benefit of leading to algebraic dispersion equations rather than to a transcendental dispersion equation; therefore, it will be easier to use than other methods such as the argument principle method, the reflection pole method, and...
Novel minimum time trajectory planning in terrain following flights
, Article IEEE Transactions on Aerospace and Electronic Systems ; Volume 43, Issue 1 , 2007 , Pages 2-12 ; 00189251 (ISSN) ; Kosari, A. R ; Sharif University of Technology
2007
Abstract
A new methodology has been proposed to enhance inverse dynamics applications in the process of trajectory planning and optimization in terrain following flights (TFFs). The new approach uses a least square scheme to solve a general two-dimensional (2-D) TFF in a vertical plane. In the mathematical process, Chebyshev polynomials are used to model the geographical data of the terrain in a given route in a manner suitable for the aircraft at hand. The aircraft then follows the modeled terrain with sufficient clearance. In this approach the terrain following (TF) problem is effectively converted to an optimal tracking problem. Results show that this method provides a flexible approach to solve...
A Chebyshev approximation for solving nonlinear integral equations of hammerstein type
, Article Applied Mathematics and Computation ; Volume 189, Issue 1 , 2007 , Pages 641-646 ; 00963003 (ISSN) ; Fattahzadeh, F ; Golpar Raboky, E ; Sharif University of Technology
2007
Abstract
A numerical method for solving Fredholm-Volterra Hammerstein integral equations is presented. This method is based on replacement of the unknown function by truncated series of well known Chebyshev expansion of functions.The quadrature formula which we use to calculate integral terms can be estimated by Fast Fourier Transform (FFT). The numerical examples and the number of operations show the advantages of this method to some other usual methods. © 2006 Elsevier Inc. All rights reserved
Stagnation-point flow of upper-convected maxwell fluids
, Article International Journal of Non-Linear Mechanics ; Volume 41, Issue 10 , 2006 , Pages 1242-1247 ; 00207462 (ISSN) ; Hajibeygi, H ; Taghavi, M ; Sharif University of Technology
2006
Abstract
Two-dimensional stagnation-point flow of viscoelastic fluids is studied theoretically assuming that the fluid obeys the upper-convected Maxwell (UCM) model. Boundary-layer theory is used to simplify the equations of motion which are further reduced to a single non-linear third-order ODE using the concept of stream function coupled with the technique of the similarity solution. The equation so obtained was solved using Chebyshev pseudo-spectral collocation-point method. Based on the results obtained in the present work, it is concluded that the well-established but controversial prediction that in stagnation-point flows of viscoelastic fluids the velocity inside the boundary layer may exceed...