Spectral Differencing with a Twist

Authors:
Richard Baltensperger;Manfred R. Trummer
Affiliations:
-;-
Venue:
SIAM Journal on Scientific Computing
Year:
2002

Citing 0
Cited 11

Higher order pseudospectral differentiation matrices

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A pseudospectral method of solution of Fisher's equation

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A spectral collocation method based on integrated Chebyshev polynomials for two-dimensional biharmonic boundary-value problems

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Tracking discontinuities in hyperbolic conservation laws with spectral accuracy

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Spectral collocation solution of a generalized Hirota-Satsuma coupled KdV equation

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Numerical solutions for constrained time-delayed optimal control problems

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Adaptive pseudospectral solution of a diffuse interface model

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Dynamics and synchronization of numerical solutions of the Burgers equation

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Higher order pseudospectral differentiation matrices

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A modified Chebyshev pseudospectral DD algorithm for the GBH equation

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Numerical solutions for some coupled nonlinear evolution equations by using spectral collocation method

Mathematical and Computer Modelling: An International Journal

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Abstract

Spectral collocation methods have become very useful in providing highly accurate solutions to differential equations. A straightforward implementation of these methods involves the use of spectral differentiation matrices. To obtain optimal accuracy these matrices must be computed carefully. We demonstrate that naive algorithms for computing these matrices suffer from severe loss of accuracy due to roundoff errors. Several improvements are analyzed and compared. A number of numerical examples are provided, demonstrating significant differences between the sensitivity of the forward problem and the inverse problem.