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In this article we investigate the stability of the finite difference schemes using the Neumann method for symmetric hyperbolic systems. For the two-dimensional symmetric hyperbolic system, the condition of the Lax-Wendroff scheme stagnation has been studied. To check for resilience usingMathCad software it has been done some calculations.

  • Read count 169
  • Date of publication 01-01-2018
  • Main LanguageIngliz
  • Pages45
Ўзбек

Ушбу мақолада симметрик гиперболик системалар учун Нейман усулидан фойдаланиб айирмали схемалар турғунлиги текширилган. Икки ўлчовли симметрик гиперболик система учун Lax-Wendroff схемасининг турғунлиги шарти ўрганилди. Турғунликни текшириш учун MathCad тизимида дастур тузилиб хисоблаш тажрибалари бажарилган.

Русский

В этой статье мы исследуем устойчивость конечноразностных схем с использованием метода Неймана для симметричных гиперболических систем. Для двумерной симметричной гиперболической системы изучено условие стагнации схемы Лакса-Вендрофа. Для проверки устойчивости с помощью программного обеспечения MathCad были выполнены некоторые расчеты

English

In this article we investigate the stability of the finite difference schemes using the Neumann method for symmetric hyperbolic systems. For the two-dimensional symmetric hyperbolic system, the condition of the Lax-Wendroff scheme stagnation has been studied. To check for resilience usingMathCad software it has been done some calculations.

№ Author name position Name of organisation
1 Sardor U.D. Senior lecturer Andijan State University
2 Raxmonov O.M. Master student
№ Name of reference
1 PD Lax & B. Wendroff, Finite difference Schemes with High Order of Solution for Hyperbolic Systems, Report NYO-9759, AEC Computing and Applied Math. Center, New York University, 1962
2 RD Richtmyer, Finite difference Methods for Initial Value Problems, Interscience Publishers, New York, 1957
3 H.-O. Kreiss. Stability theory for di ff Neutral approximations of mixed initial boundary value problems. I. Math. Comp., 22: 703-714, 1968
4 Harten A. On the symmetric form of systems of conservation laws with enthropy. J. Comput. Phys. 1983. V. 49, 1, p.151-164
5 Svetlana Selivanova . Victor Selivanov. Computing ing the Solution Operators of Symmetric Hyperbolic Systems of PDE. Journal of Universal Computer Science, vol. 15, no. 6 (2009)
6 Jean-Francois Coulombel. Stability of fi nite di ff Neutral schemes for hyperbolic initial boundary value problems. France 2009 y
7 Joel A.Tropp "An elementary proof of the spectral radius formula for matrices". 2001.
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