 ### Journals Information

Mathematics and Statistics Vol. 7(3), pp. 82 - 89
DOI: 10.13189/ms.2019.070305
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## The Difference Splitting Scheme for Hyperbolic Systems with Variable Coefficients

Aloev R. D. 1,*, Eshkuvatov Z. K. 2, Khudoyberganov M. U. 1, Nematova D. E. 1
1 Faculty of Mathematics, National University of Uzbekistan (NUUz), Tashkent, Uzbekistan
2 Faculty of Science and Technology, Universiti Sains Islam Malaysia (USIM), Negeri Sembilan, Malaysia

ABSTRACT

In the paper, we propose a systematic approach to design and investigate the adequacy of the computational models for a mixed dissipative boundary value problem posed for the symmetric t-hyperbolic systems. We consider a two-dimensional linear hyperbolic system with variable coefficients and with the lower order term in dissipative boundary conditions. We construct the difference splitting scheme for the numerical calculation of stable solutions for this system. A discrete analogue of the Lyapunov's function is constructed for the numerical verification of stability of solutions for the considered problem. A priori estimate is obtained for the discrete analogue of the Lyapunov's function. This estimate allows us to assert the exponential stability of the numerical solution. A theorem on the exponential stability of the solution of the boundary value problem for linear hyperbolic system and on stability of difference splitting scheme in the Sobolev spaces was proved. These stability theorems give us the opportunity to prove the convergence of the numerical solution.

KEYWORDS
Difference Scheme, Lyapunov Function, Mixed Problem, Stability

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
 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, No. 3, pp. 82 - 89, 2019. DOI: 10.13189/ms.2019.070305.

(b). APA Format:
Aloev R. D. , Eshkuvatov Z. K. , Khudoyberganov M. U. , Nematova D. E. (2019). The Difference Splitting Scheme for Hyperbolic Systems with Variable Coefficients. Mathematics and Statistics, 7(3), 82 - 89. DOI: 10.13189/ms.2019.070305.