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A review of pseudospectral methods for solving partial differential equations

Published online by Cambridge University Press:  07 November 2008

Bengt Fornberg and
David M. Sloan
Bengt Fornberg
Affiliation:
Corporate ResearchExxon Research and Engineering Company Annandale, NJ 08801, USA E-mail: bfornbe@erenj.com
David M. Sloan
Affiliation:
Department of MathematicsUniversity of StrathclydeGlasgow G1 1XH, Scotland E-mail: caas10@computer-centre-sun.strathclyde.ac.uk
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Finite Difference (FD) methods approximate derivatives of a function by local arguments (such as du(x) / dx ≈ (u(x + h) − u(x − h))/2h, where h is a small grid spacing) – these methods are typically designed to be exact for polynomials of low orders. This approach is very reasonable: since the derivative is a local property of a function, it makes little sense (and is costly) to invoke many function values far away from the point of interest.

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Research Article
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Acta Numerica , Volume 3 , January 1994, pp. 203 - 267
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Copyright © Cambridge University Press 1994

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References

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