Closed-form expressions for the finite approximations of first and higher derivatives based on Taylor series
Ishtiaq Rasool Khan,Ryoji Ohba +1 more
TLDR
In this paper, a comparison of the three types of approximations is given with an ideal digital differentiator by comparing their frequency responses, which reveals that the central difference approximation can be used as digital differentiators, because they do not introduce any phase distortion and their amplitude response is closer to that of an ideal differentiator.About:
This article is published in Journal of Computational and Applied Mathematics.The article was published on 1999-07-31 and is currently open access. It has received 69 citations till now. The article focuses on the topics: Finite difference & Taylor series.read more
Citations
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Journal ArticleDOI
Applied Numerical Analysis. By C.F. Gerald. Pp. xii, 340. £3·60. 1970. (Addison-Wesley.)
Journal ArticleDOI
General explicit difference formulas for numerical differentiation
TL;DR: The generalized Vandermonde determinant is introduced, and general explicit finite difference formulas with arbitrary order accuracy for approximating first and higher derivatives, which are applicable to unequally or equally spaced data are presented.
Journal ArticleDOI
Discrete-Time Fractional-Order PID Controller: Definition, Tuning, Digital Realization and Some Applications
TL;DR: A discrete-time version of the FOPID controller that applies nonlocal operators (with adjustable memory length) to the error signal and has the capacity of solving complicated control problems is proposed.
Journal ArticleDOI
New finite difference formulas for numerical differentiation
Istiaq Rasool Khan,Ryoji Ohba +1 more
TL;DR: In this paper, the authors presented new finite difference formulas, which are more accurate than the available ones, especially for the oscillating functions having frequency components near the Nyquist frequency.
Journal ArticleDOI
Controlling the numerical Cerenkov instability in PIC simulations using a customized finite difference Maxwell solver and a local FFT based current correction
Fei Li,Peicheng Yu,Xinlu Xu,Frederico Fiuza,Viktor Decyk,Thamine Dalichaouch,Asher Davidson,Adam Tableman,Weiming An,Frank Tsung,Ricardo Fonseca,Ricardo Fonseca,Wei Lu,Warren Mori +13 more
TL;DR: It is shown that FFTs can be performed locally to current on each partition to filter out the main and first spatial aliasing NCI modes, and to correct the current so that it satisfies the continuity equation for the customized spatial derivative, which ensures that Gauss’ Law is satisfied.
References
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Discrete-Time Signal Processing
TL;DR: In this paper, the authors provide a thorough treatment of the fundamental theorems and properties of discrete-time linear systems, filtering, sampling, and discrete time Fourier analysis.
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Numerical Analysis
TL;DR: This report contains a description of the typical topics covered in a two-semester sequence in Numerical Analysis, and describes the accuracy, efficiency and robustness of these algorithms.
MonographDOI
Introduction to Numerical Analysis
TL;DR: 1. The numerical evaluation of expressions 2. Linear systems of equations 3. Interpolation and numerical differentiation 4. Numerical integration 5. Univariate non linear equations 6. Systems of nonlinear equations.
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Advanced Engineering Mathematics
TL;DR: This book discusses ODEs, Partial Differential Equations, Fourier Series, Integrals, and Transforms, and Numerics for ODE's and PDE's, as well as numerical analysis and potential theory, and more.