ISSN:
1573-7691
Keywords:
Interpolation error
;
Fourier method
;
Chebyshev method
;
pseudospectral method
Source:
Springer Online Journal Archives 1860-2000
Topics:
Computer Science
Notes:
Abstract The error in Chebyshev or Fourier interpolation is the product of a rapidly varying factor with a slowly varying modulation. This modulation is the “envelope” of the error. Because this slow modulation controls the amplitude of the error, it is crucial to understand this “error envelope.” In this article, we show that the envelope varies strongly withx, but its variations can be predicted from the convergence-limiting singularities of the interpolated function f(x). In turn, this knowledge can be translated into a simple spectral correction algorithm for wringing more accuracy out of the same pseudospectral calculation of the solution to a differential equation.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01063120
