A dispersion analysis for difference schemes: tables of generalized Airy functions
HTML articles powered by AMS MathViewer
- by R. C. Y. Chin and G. W. Hedstrom PDF
- Math. Comp. 32 (1978), 1163-1170 Request permission
Abstract:
This paper contains graphs and tables of the function \[ A{i_{p,q}}(\alpha ,x) = \int _{ - \infty }^\infty {{{(2\pi )}^{ - 1}}\exp \{ i{y^p}/p - \alpha {y^q}/q + ixy\} \;dy} \] and its indefinite integral for $p = 3,5,7$, for $q = 2,4,6$, and for several values of $\alpha$ with $\alpha \geqslant 0$. It is shown how these tables should influence the choice of an artificial viscosity for a difference scheme for a linear hyperbolic equation.References
-
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.
- Raymond C. Y. Chin, Dispersion and Gibbs phenomenon associated with difference approximations to initial boundary-value problems for hyperbolic equations, J. Comput. Phys. 18 (1975), no. 3, 233–247. MR 391530, DOI 10.1016/0021-9991(75)90001-7 JACOB E. FROMM, "A method for reducing dispersion in convective difference schemes," J. Computational Phys., v. 3, 1968, pp. 176-189.
- G. W. Hedstrom, Models of difference schemes for $u_{t}+u_{x}=0$ by partial differential equations, Math. Comp. 29 (1975), no. 132, 969–977. MR 388797, DOI 10.1090/S0025-5718-1975-0388797-4 G. W. HEDSTROM, Generalized Airy Functions and Artificial Viscosities, Lawrence Livermore Laboratory report UCRL-78042. 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.
- 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 319382, DOI 10.3402/tellusa.v24i3.10634 YUDELL L. LUKE, The Special Functions and their Approximations, vol. 1, Academic Press, New York, 1969. MR 39 #3039. R. D. RICHTMEYER & K. W. MORTON, Difference Methods for Initial Value Problems, 2nd ed., Interscience, New York, 1967. MR 36 #3515.
- 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 284018
- R. F. Warming and B. J. Hyett, The modified equation approach to the stability and accuracy analysis of finite-difference methods, J. Comput. Phys. 14 (1974), 159–179. MR 339526, DOI 10.1016/0021-9991(74)90011-4
Additional Information
- © Copyright 1978 American Mathematical Society
- Journal: Math. Comp. 32 (1978), 1163-1170
- MSC: Primary 65M10
- DOI: https://doi.org/10.1090/S0025-5718-1978-0494982-6
- MathSciNet review: 0494982