Malaysian Journal of Mathematical Sciences, January 2022, Vol. 16, No. 1
The Difference Splitting Scheme for \(n\)-Dimensional Hyperbolic Systems
Aloev R. D., Eshkuvatov Z. K., Khudoyberganov M. U., and Nematova D. E.
Corresponding Email: aloevr@mail.ru
Received date: 10 March 2020
Accepted date: 14 October 2021
Abstract:
In this paper, we propose the difference splitting scheme for a mixed problem posed for \(n\) -dimensional symmetric $t$-hyperbolic systems. We construct the difference splitting scheme for the numerical calculation of stable solutions for this system. To build a difference scheme, a multidimensional problem is split into one-dimensional ones and solved for each direction. A discrete analogue of the Lyapunov's function is constructed for the numerical verification of stability 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 solution of the boundary value problem for linear hyperbolic system was proved. These stability theorems give us the opportunity to prove the convergence of the numerical solution.
Keywords: multidimensional hyperbolic systems; stability; difference scheme; splitting scheme
Indexing
