ICOSAHOM 95: Proceedings of the Third International by Andrew V. Ilin, L. Ridgway Scott (Eds.)

By Andrew V. Ilin, L. Ridgway Scott (Eds.)

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Huld, G. Knorr and 1379. S. Tuckerman,Transforrnations of matricesinto banded form, J. 84 (1989), pp. 360-376. P. Lynov. Spectral Methods in Numerical Plasma Simulation,Phys. Scripta40 (1989), pp. 270-279. A. Coutsias, T. Hagstrom and D. Torres, An algorithm for the efficient spectralsolution of linear ordinary differential equationswith rational function eoefcients, NASA TechnicalMemorandum 106762, ICOMP-94-25, (1994). methodsfor [71B. Fornberg, A review of pseudospectral A Hypergeometric recurrence re- lations Hypergeometricfunctionssatisfy the differentialequation (62)z(1- z)•d2F q-[c-(aq-bq1)z] •zz dF- abF = 0 solvingpartial differential equations,Acta Numerica where a, b, and c are parameters and F represents (1994), pp.

Additionally, we will addressthe issuesof solutionof implicit problems,the determination of the initial vorticity distribution, and the questionof full discretestability of the proposedscheme. •1 matricesof •own exposion coefficients. (6)-(7). ], becomes a two-dimensional convolution in An Accurate Tau Method For IncompressibleFlows 45 m6de space. However, in order to avoid the significant In constructingan approximatesolutionto this problem, computational load required to calculate the convolution, usinga Chebyshevtau method, we look for solutionsto the derivativesare calculatedin mode space;whereasthe LM2 = ] , convolution is done in point-space, where it amounts to a pointwise multiplication.

Asshownin [8], the conditioningof the integrationoperatoris very good, leadingus to the conclusion that the full problemmay be solvedwith very high accuracyevenat high resolution. 1 Poisson's equation Assuming • = D~2q• •aoneobtainsthescheme <35) .. [I-

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