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), 1163-1170

MSC:
Primary 65M10

DOI:
https://doi.org/10.1090/S0025-5718-1978-0494982-6

MathSciNet review:
0494982

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Abstract | References | Similar Articles | Additional Information

Abstract: This paper contains graphs and tables of the function

**[1]**JAY P. BORIS & DAVID L. BOOK, "Flux-corrected transport. I. SHASTA, A fluid transport algorithm that works,"*J. Computational Phys.*, v. 11, 1973, pp. 38-69.**[2]**Raymond C. Y. Chin,*Dispersion and Gibbs phenomenon associated with difference approximations to initial boundary-value problems for hyperbolic equations*, J. Computational Phys.**18**(1975), no. 3, 233–247. MR**0391530****[3]**JACOB E. FROMM, "A method for reducing dispersion in convective difference schemes,"*J. Computational Phys.*, v. 3, 1968, pp. 176-189.**[4]**G. W. Hedstrom,*Models of difference schemes for 𝑢_{𝑡}+𝑢ₓ=0 by partial differential equations*, Math. Comp.**29**(1975), no. 132, 969–977. MR**0388797**, https://doi.org/10.1090/S0025-5718-1975-0388797-4**[5]**G. W. HEDSTROM,*Generalized Airy Functions and Artificial Viscosities*, Lawrence Livermore Laboratory report UCRL-78042.**[6]**A. C. HINDMARSH, GEAR:*Ordinary Differential Equation System Solver*, Lawrence Livermore Laboratory report UCID-30001, Rev. 1, A. C.C. No. 592, GEAR, Argonne Code Center, Building 221, Argonne National Laboratory, Argonne, I11.**[7]**Heinz-Otto Kreiss and Joseph Oliger,*Comparison of accurate methods for the integration of hyperbolic equations*, Tellus**24**(1972), 199–215 (English, with Russian summary). MR**0319382**, https://doi.org/10.3402/tellusa.v24i3.10634**[8]**YUDELL L. LUKE,*The Special Functions and their Approximations*, vol. 1, Academic Press, New York, 1969. MR**39**#3039.**[9]**R. D. RICHTMEYER & K. W. MORTON,*Difference Methods for Initial Value Problems*, 2nd ed., Interscience, New York, 1967. MR**36**#3515.**[10]**S. I. Serdjukova,*The oscillations that arise in numerical calculations of the discontinuous solutions of differential equations*, Ž. Vyčisl. Mat. i Mat. Fiz.**11**(1971), 411–424 (Russian). MR**0284018****[11]**R. F. Warming and B. J. Hyett,*The modified equation approach to the stability and accuracy analysis of finite-difference methods*, J. Computational Phys.**14**(1974), 159–179. MR**0339526**

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1978-0494982-6

Article copyright:
© Copyright 1978
American Mathematical Society