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Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

Abstract

We give numerical examples demonstrating and confirming the theoretical results obtained for systems of two linear hyperbolic equations.

First Page

83

Last Page

92

References

1. Godunov S.K., Equations of mathematical physics. M.: Nauka, 1979, 372 p.

2. Bastin G., Coron J.M. Stability and Boundary Stabilization of 1-D Hyperbolic Systems. Progress in Nonlinear Differential Equations and Their Applications, Birkhauser Basel press. Vol. 88, 2016, pp. 220.

2. Simone Gottlich, Peter Schillen. Numerical Discretization of Boundary Control Problems for Systems of Balance Laws: Feedback Stabilization. University of Mannheim, Germany, 2017.

3. Blokhin A.M., Aloev R.D. Energy integrals and their applications to the study of the stability of the difference schemes. Novosibirsk State University Press, 1993, 224 p.

4. Aloev R.D., Eshkuvatov Z.K., Davlatov Sh.O., Nik Long N.M.A. Sufficient condition of stability of finite element method for symmetric t-hyperbolic systems with constant coefficients. Computers and Mathematics with Applications, Vol. 68, 2014, pp. 1194-1204.

5. Aloev R.D., A.M. Blokhin, M.U. Hudayberganov One Class of Stable Difference Schemes for Hyperbolic System. American Journal of Numerical Analysis. Vol. 2, 2014, pp. 85-89.

6. Aloev R.D., Davlatov Sh.O., Eshkuvatov Z. K., Nik Long N.M.A. Uniqueness solution of the finite elements scheme for symmetric hyperbolic systems with variable coefficients. Malaysian Journal of Mathematical Sciences (MJMS), 10(S), 2016, pp. 49-60.

7. Aloev R.D., Khudoyberganov M. U., Blokhin A.M. Construction and research of adequate computational models for quasilinear hyperbolic systems. Numerical Algebra, Control and Optimization. Vol. 8, 2018. pp. 287-299.

8. Aloev R.D., Eshkuvatov Z.K., Khudayberganov M. U., Nik Long N.M.A. A discrete analogue of energy integral for a difference scheme for quasilinear hyperbolic systems. Applied Mathematics, Vol. 9, 2018, pp. 789-805.

9. Aloev R.D., Eshkuvatov Z.K., Khudoyberganov M.U., Nematova D.E. The Difference Splitting Scheme for Hyperbolic Systems with Variable Coefficients. Mathematics and Statistics. Vol. 7, 2019, pp. 82-89, DOI: 10.13189/ms.2019.070305.

10. Amaury Hayat, Peipei Shang. A quadratic Lyapunov function for Saint-Venant equations with arbitrary friction and space-varying slope. 2018.

11. Georges Bastin and Jean-Michel Coron. Stability and Boundary Stabilisation of 1-D Hyperbolic Systems. Number 88in Progress in Nonlinear Differential Equations and Their Applications. Springer International, 2016.

12. Georges Bastin and Jean-Michel Coron. A quadratic Lyapunov function for hyperbolic density-velocity systems with nonuniform steady states. Systems & Control Letters, 104:66, 2017.

13. Georges Bastin, Jean-Michel Coron, and Brigitte d'Andrea Novel. On lyapunov stability of linearised saint-venant equations for a sloping channel. Networks and Heterogeneous Media, 4:177, 2009.

14. Miroslav Krstic and Andrey Smyshlyaev. Boundary Control of PDEs: A Course on Backstepping Designs, volume 16 of Advances in Design and Control. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2008.

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