Gibbs phenomenon in the Hermite interpolation on the circle

Berriochoa, E.; Cachafeiro, A.; Díaz, J.

doi:10.1016/j.amc.2014.12.063

Cited by 7 publications

(2 citation statements)

References 9 publications

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“…The corresponding degrees of approximation are provided that show that the obtained nodal matrix is almost optimal. In Berriochoa et al [36], a few applications of the Hermite interpolation are reported.…”

Section: Literature Review On Hermite Polynomialsmentioning

confidence: 99%

Survey of Hermite Interpolating Polynomials for the Solution of Differential Equations

Kumari

Kukreja

2023

Mathematics

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With progress on both the theoretical and the computational fronts, the use of Hermite interpolation for mathematical modeling has become an established tool in applied science. This article aims to provide an overview of the most widely used Hermite interpolating polynomials and their implementation in various algorithms to solve different types of differential equations, which have important applications in different areas of science and engineering. The Hermite interpolating polynomials, their generalization, properties, and applications are provided in this article.

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Section: Literature Review On Hermite Polynomialsmentioning

confidence: 99%

Survey of Hermite Interpolating Polynomials for the Solution of Differential Equations

Kumari

Kukreja

2023

Mathematics

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“…So, Gibbs oscillations occur. In order to eliminate Gibbs oscillation, multiplier named as Gibbs factor is inserted in the calculations [13][14][15].…”

Section: Introductionmentioning

confidence: 99%

The Effect of GIBBS Factor on Transient Analysis in Underground Power Cables

Uyaroğlu

Emiroğlu

2019

Sakarya University Journal of Science

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In this work, the transient overvoltage phenomena occurred at 34.5 kV AC underground cable transmission systems during the closure of the underground cables is to be studied and simulated by using the MATLAB program. Then, the transient voltage occurred at the underground cables is analyzed by using a modified Fourier transform. The studied system of underground cables is firstly modeled in the frequency domain. Transient voltages induced at the sending-end and receiving-end terminals of an underground cable of the transmission system are calculated in the frequency domain and using inverse Fourier Transform, the sending end and receiving end voltages are obtained by converting to the time domain. The effects of Gibbs factor on transients overvoltage phenomena considering cable length and source impedance are investigated. Numerical simulations are presented to demonstrate the transient voltages induced at the terminals of sending-end and receiving-end of an underground cable at the transmission system and the effects of Gibbs factor to eliminate Gibbs oscilllations.

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