One Class of Stable Difference Schemes for Hyperbolic System

A.M. Blokhin¹, R.D. Alaev² and M.U. Hudayberganov^2,

¹Differential Equations, Novosibirsk Institute of Mathematics, Novosibirsk, Russian

²Computations technologies and mathematical modeling, National University of Uzbekistan, Tashkent, Uzbekistan

Cite this paper:
A.M. Blokhin, R.D. Alaev and M.U. Hudayberganov. One Class of Stable Difference Schemes for Hyperbolic System. American Journal of Numerical Analysis. 2014; 2(3):85-89. doi: 10.12691/ajna-2-3-4

Abstract

It is suggested one class of difference schemes for hyperbolic systems of equations, which have several forms of writing. Stability of suggested difference schemes is investigated with the help of technics of integrals energy. Numerical results of model problems are given.

Keywords:
hyperbolic system difference schemes stability energy norm

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References:

[1]	Blokhin A.M., Aloev R.D. Energy integrals and thier applications to investigation of stability of difference schemes. Novosibirsk, 1993. 224 p.
[2]	Kulikovskii A.G., Pogorelov N.V., Semenov A.Yu. Mathematical problems of numerical solution of hyperbolic systems. M.:Physics and mathematics publishers, 2001, 608 p.
[3]	Blokhin A.M., Sokovikov I.G. About one approach to formulation of difference schemes for quasi-linear equations of gas dynamics. Siberian Mathematical Journal, 1999, V.40, № 6, Pp.1236-1243.
[4]	Harten A. On the symmetric form of systems of conservation laws with enthropy. J. Comput. Phys. 1983. V. 49, № 1, p.151-164.