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Gibbs phenomenon removal by adding Heaviside functions

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Abstract

We define a kind of spectral series to filter off completely the Gibbs phenomenon without overshooting and distortional approximation near a point of discontinuity. The construction of this series is based on the method of adding the Fourier coefficients of a Heaviside function to the given Fourier partial sums. More precisely, we prove the uniform convergence of the proposed series on the class of piecewise smooth functions. Also, we attach two numerical examples which illustrate the uniform convergence of the suggested series in comparison with the Fourier partial sums.

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Authors and Affiliations

  1. Department of Mathematics, Sogang University, Seoul, 121-742, Korea

    Kyung Soo Rim

  2. Department of Infor. & Stat., Kunsan National University, Kunsan, 573-701, Korea

    Beong In Yun

Authors
  1. Kyung Soo Rim
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  2. Beong In Yun
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Correspondence to Kyung Soo Rim.

Additional information

Communicated by Qiyu Sun.

The research of Kyung Soo Rim was supported in part by the grants, Seoul R&D Program: ST100025

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Rim, K.S., Yun, B.I. Gibbs phenomenon removal by adding Heaviside functions. Adv Comput Math 38, 683–699 (2013). https://doi.org/10.1007/s10444-011-9255-7

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  • DOI: https://doi.org/10.1007/s10444-011-9255-7

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