Abstract
For a nonlinear transport model, we propose a simple and economical two-step algorithm that decreases the dimension of the system of nonlinear equations, as compared with implicit difference schemes. We prove theorems on necessary conditions for stability with respect to the initial data for the nonlinear problem and theorems on sufficient conditions for stability in the case of the linearized model. We also obtain theorems on approximation of the integral conservation law on a grid. The necessary condition obtained is a condition on the coefficients of the differential equation (which singles out an admissible class of equations) but not a condition on the ratio of the grid steps. Bibliography: 3 titles.
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References
A. E. Grishchenko, L. P. Zinchuk, and V. S. Kas'yanyuk,On a difference method of solution of nonlinear boundary-value problems, Deposit of Scientific Manuscripts, # 1615, Uk. 84, 03.10.1984.
P. Roache,Computational Fluid Dynamics, Hermosa Publishers, Albuquerque (1978).
R. D. Richtmyer and K. W. Morton,Difference Methods for Initial-Value Problems, New York-London-Sydney (1967).
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Translated fromObchyslyuval'na ta Prykladna Matematyka, No. 81, 1997, pp. 25–32.
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Gryshchenko, O.Y. A study of a numerical algorithm for a nonlinear transport model. J Math Sci 102, 3742–3748 (2000). https://doi.org/10.1007/BF02680227
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DOI: https://doi.org/10.1007/BF02680227