The Difference Splitting Scheme for Hyperbolic Systems with Variable Coefficients
| Autor: | D.E. Nematova, R.D. Aloev, M.U. Khudoyberganov, Zainidin K. Eshkuvatov |
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| Rok vydání: | 2019 |
| Předmět: |
Statistics and Probability
Lyapunov function Economics and Econometrics A priori estimate Function (mathematics) Stability (probability) Sobolev space symbols.namesake Exponential stability Dissipative system symbols Applied mathematics Boundary value problem Statistics Probability and Uncertainty Mathematics |
| Zdroj: | Mathematics and Statistics. 7:82-89 |
| ISSN: | 2332-2144 2332-2071 |
| DOI: | 10.13189/ms.2019.070305 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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