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Gottlieb, D. and Shu, C.W. (1994 ) On The Gibbs Phenomenon V: Recovering Exponential Accuracy in a Sub-Interval from a Gegenbauer Partial Sum of a Piecewise Analytic Function. NASA Contractor Report 194952, ICASE Report No. 94-61.

has been cited by the following article:

• TITLE: A Spectral Finite Difference Method for Analysis of a Fluid-Lubricated Herringbone Grooves Journal Bearing under a Special Case at Rectangle Groove

  AUTHORS: Jun Liu

  KEYWORDS: Fluid-Lubricated, Herringbone Grooves, Journal Bearing, Spectral Difference Scheme, Fourier Series, Gibbs Phenomenon

  JOURNAL NAME: Applied Mathematics, Vol.10 No.12, December 11, 2019

  ABSTRACT: A spectral difference method is applied to get numerical solutions for a fluid-lubricated herringbone grooved journal bearing with trapezoidal grooves by previous work of the authors. However, an inexpedience in which Fourier series of the film profile does not converge at jump points of groove start or groove end in the case of rectangle groove was still remained. In the paper, an inexpedience of numerical analysis under a special case at rectangle groove is challenged to solve. As a result, for compensation of which Fourier series does not converge at jump points in a special case of rectangle groove, Fourier coefficient of fluid film thickness is proposed as taking the limit of which in a case trapezoidal groove at trapezoidal angle approaches 0.