Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Instability and stability of numerical approximations to discrete velocity models of the Boltzmann equation

Author: Robert Peszek
Journal: Quart. Appl. Math. 54 (1996), 777-791
MSC: Primary 82C40; Secondary 35Q99, 39A11, 65M12
DOI: https://doi.org/10.1090/qam/1417239
MathSciNet review: MR1417239
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Abstract: We study a standard, explicit finite difference approximation of the 2-D Broadwell model and construct a numerical solution with the sum-norm growing in time faster than any polynomial. Our construction is based on a structure of a self-similar fractal!

References [Enhancements On Off] (What's this?)

  • [1] T. Płatkowski and R. Illner, Discrete velocity models of the Boltzmann equation: A survey of mathematical aspects of the theory, SIAM Review 30, 213-255 (1988)
  • [2] R. Illner, Global existence results for discrete velocity models of the Boltzmann equation in several dimensions, J. Méch. Théor. Appl. 1, 611-622 (1982)
  • [3] R. Illner, Examples of non-bounded solutions in discrete kinetic theory, J. Méch. Théor. Appl. 5, 561-571 (1986)
  • [4] S. Kawashima, Global solution of the initial value problem for a discrete velocity model of the Boltzmann equation, Proc. Japan Acad. Ser. A. Math. Sci. 57, 1-24 (1981)
  • [5] R. Peszek, Convergence of numerical solutions to systems of semilinear hyperbolic equations, manuscript (1993)
  • [6] B. B. Mandelbrot, The Fractal Geometry of Nature, W. H. Freeman and Company, New York, 1983

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DOI: https://doi.org/10.1090/qam/1417239
Article copyright: © Copyright 1996 American Mathematical Society

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