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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Three-dimensional second-order accurate difference schemes for discontinuous hydrodynamic flows
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by Ephraim L. Rubin and Stanley Preiser PDF
Math. Comp. 24 (1970), 57-63 Request permission


In this paper, we show how a second-order accurate two-step method used in the numerical computation of hydrodynamic flows may be derived directly from the integral conservation laws. A necessary and sufficient condition for stability for the linearized equations is derived for the three-dimensional Cartesian coordinate case.
    J. L. Anderson, S. Preiser & E. L. Rubin, "Conservation form of the equations of hydrodynamics in curvilinear coordinate systems," J. Computational Phys., v. 2, 1968, pp. 279–287.
  • Peter Lax and Burton Wendroff, Systems of conservation laws, Comm. Pure Appl. Math. 13 (1960), 217–237. MR 120774, DOI 10.1002/cpa.3160130205
  • R. D. Richtmyer, A Survey of Difference Methods for Non-Steady Fluid Dynamics, NCAR Technical Note 63–2, 1962. E. L. Rubin & S. Z. Burstein, "Difference methods for the inviscid and viscous equations of a compressible gas," J. Computational Phys., v. 2, 1967, pp. 178–196.
  • C. Truesdell and R. Toupin, The classical field theories, Handbuch der Physik, Bd. III/1, Springer, Berlin. With an appendix on tensor fields by J. L. Ericksen. MR 0118005
  • A. H. Taub, On the Derivation of Difference Equations for Hydrodynamics, Los Alamos Scientific Laboratory Report LA-2073, 1957.
  • Luther Pfahler Eisenhart, Continuous groups of transformations, Dover Publications, Inc., New York, 1961. MR 0124008
  • Heinz-Otto Kreiss, On difference approximations of the dissipative type for hyperbolic differential equations, Comm. Pure Appl. Math. 17 (1964), 335–353. MR 166937, DOI 10.1002/cpa.3160170306
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Additional Information
  • © Copyright 1970 American Mathematical Society
  • Journal: Math. Comp. 24 (1970), 57-63
  • MSC: Primary 76.65
  • DOI:
  • MathSciNet review: 0264904