On the accuracy of pseudospectral differentiation

Abstract

For various grids on a finite interval we measure the accurarcy of pseudospectral (collocation) differentiation matrices using two parameters. The first one is the rank defficiency of the differentation matrices. The second one quantifies the extent at which such matrices transform a constant vector into the null vector.

Authors

C.I. Gheorghiu
Tiberiu Popoviciu Institute of Numerical Analysis

Keywords

pseudospectral differentiation; Chebyshev-Gauss-Lobatto grid; Legendre grid; equidistant grid; accuracy; floating-point arithmetic

References

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Paper coordinates

C.I. Gheorghiu,  On the accuracy of pseudospectral differentiation, ROMAI J., 10 (2014) no. 1, pp. 55-62.

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Journal

ROMAI J.

Publisher Name
Paper on journal website
Print ISSN

2065-7714

Online ISSN

1841-5512

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References

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References

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[3] Gheorghiu, C.I.,  Spectral Methods for Differential Problems,  Casa Cartii de Stiinta Publishing House, Cluj-Napoca, 2007.

[4] Gheorghiu, C. I., Spectral  Methods for Non-Standard Eigenvalue Problems. Fluid and Structural Mechanics and Beyond,  Springer Briefs in Mathematics, 2014.

[5] Gottlieb, D., Orszag, S.A.,  Numerical Analysis of Spectral Methods: Theory and Applications, I SIAM Philadelphia, 1977.

[6] Henrici, P., Applied and Computational Complex Analysis: Discrete Fourier Analysis-Cauchy Integrals-Construction of
Conformal Maps-Univalent Functions, Vol. 3 John Wiley and Sons, Inc., New York, 1986.

[7] Weideman, J.A.C., Reddy, S.C. A MATLAB Differentiation Matrix Suite, ACM Trans, on Math. Software, 26, 465-519 (2000)

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