A dispersion analysis for difference schemes: tables of generalized Airy functions
Authors:
R. C. Y. Chin and G. W. Hedstrom
Journal:
Math. Comp. 32 (1978), 11631170
MSC:
Primary 65M10
MathSciNet review:
0494982
Fulltext PDF Free Access
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Abstract: This paper contains graphs and tables of the function and its indefinite integral for , for , and for several values of with . It is shown how these tables should influence the choice of an artificial viscosity for a difference scheme for a linear hyperbolic equation.
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 JAY P. BORIS & DAVID L. BOOK, "Fluxcorrected transport. I. SHASTA, A fluid transport algorithm that works," J. Computational Phys., v. 11, 1973, pp. 3869.
 [2]
 RAYMOND C. Y. CHIN, "Dispersion and Gibbs phenomenon associated with difference approximations to initial boundaryvalue problems for hyperbolic equations," J. Computational Phys., v. 18, 1975, pp. 233247. MR 0391530 (52:12351)
 [3]
 JACOB E. FROMM, "A method for reducing dispersion in convective difference schemes," J. Computational Phys., v. 3, 1968, pp. 176189.
 [4]
 G. W. HEDSTROM, "Models of difference schemes for by partial differential equations," Math. Comp., v. 29, 1975, pp. 969977. MR 0388797 (52:9631)
 [5]
 G. W. HEDSTROM, Generalized Airy Functions and Artificial Viscosities, Lawrence Livermore Laboratory report UCRL78042.
 [6]
 A. C. HINDMARSH, GEAR: Ordinary Differential Equation System Solver, Lawrence Livermore Laboratory report UCID30001, Rev. 1, A. C.C. No. 592, GEAR, Argonne Code Center, Building 221, Argonne National Laboratory, Argonne, I11.
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 H.O. KREISS & J. OLIGER, "Comparison of accurate methods for the integration of hyperbolic equations," Tellus, v. 24, 1972, pp. 199215. MR 47 #7926. MR 0319382 (47:7926)
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 YUDELL L. LUKE, The Special Functions and their Approximations, vol. 1, Academic Press, New York, 1969. MR 39 #3039.
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 R. D. RICHTMEYER & K. W. MORTON, Difference Methods for Initial Value Problems, 2nd ed., Interscience, New York, 1967. MR 36 #3515.
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 S. I. SERDJUKOVA, "The oscillations that arise in numerical calculations of the discontinuous solutions of differential equations," Ž. Vyčisl. Mat. i Mat. Fiz., v. 11, 1971, pp. 411424 = U.S.S.R. Comput. Math. and Math Phys., v. 11, 1971, pp. 140154. MR 44 #1248. MR 0284018 (44:1248)
 [11]
 R. F. WARMING & B. J. HYETT, "The modified equation approach to the stability and accuracy of finitedifference methods," J. Comput. Phys., v. 14, 1974, pp. 159179. MR 49 #4284. MR 0339526 (49:4284)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718197804949826
PII:
S 00255718(1978)04949826
Article copyright:
© Copyright 1978
American Mathematical Society
