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 | References | Similar Articles | Additional Information

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!

**[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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Additional Information

DOI:
https://doi.org/10.1090/qam/1417239

Article copyright:
© Copyright 1996
American Mathematical Society