•  
  •  
 

Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences

Abstract

In this paper we consider a class of quasi-linear hyperbolic systems, which allows the construction of a dissipative energy integrals. In the basis of the design and investigation the stability of difference schemes for the numerical solution of the initial boundary value problems for the above class of quasi-linear hyperbolic systems, we put the existence of a discrete analogue of the dissipative energy integrals.

First Page

1

Last Page

13

References

1. Blokhin A. M., Aloev R. D. Energy integrals and their applications to investigation of stability of difference schemes. Novosibirsk, 1993. – 224 p.

2. Godunov S. K. Equations of mathematical physics. Nauka, Moscow, 1979 (in Russian). – 392 p.

3. Zavyalov Yu. S., Kvasov B. I., Miroshnichenko V. L. Methods of spline functions. Moscow, Nauka, 1980 (in Russian). – 352 p.

4. Godunov S. K. An interesting class of quasi-linear systems. Dokl. Akad. Nauk SSSR, 1961, V.139, No.3, pp.521–523 (in Russian).

5. Godunov S. K., Romenskii E. I. Elements of continuum mechanics and conservation laws. Springer-Verlag, New York, 2003. – 258 p.

6. Vol'pert A. I., Khudyaev S. I. On the Cauchy problem for composite systems of nonlinear differential equations. Math. USSR Sb., 1972, V.16, No.4, pp.517–544.

7. Harten A. On the symmetric form of systems of conservation laws with entropy. J. Comp. Phys., 1983, V.49, pp.151–164.

8. 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, 2014, V.68, No.10, pp.1194–1204.

9. Aloev R. D., Blokhin A. M., Hudayberganov M. U. One Class of Stable Difference Schemes for Hyperbolic System, American Journal of Numerical Analysis, 2014, V.2, No.3, pp.85–9.

Share

COinS
 
 

To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.