n维双曲型系统的差分分裂格式

IF 0.5 Q3 MATHEMATICS Malaysian Journal of Mathematical Sciences Pub Date : 2022-01-31 DOI:10.47836/mjms.16.1.01
Aloev R. D., Eshkuvatov Z., Khudoyberganov M. U., Nematova D. E.
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引用次数: 0

摘要

本文给出了一类n维对称t-双曲型系统混合问题的差分分裂格式。构造了该系统稳定解数值计算的差分分割格式。为了建立差分格式,将一个多维问题分解成一维问题,并在每个方向上求解。构造了李雅普诺夫函数的离散模拟,用于所考虑问题的稳定性解的数值验证。对李雅普诺夫函数的离散模拟得到了一个先验估计。这个估计使我们能够断言数值解的指数稳定性。证明了线性双曲型系统边值问题指数稳定性解的一个定理。这些稳定性定理使我们有机会证明数值解的收敛性。
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The Difference Splitting Scheme for n-Dimensional Hyperbolic Systems
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.
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来源期刊
CiteScore
1.10
自引率
20.00%
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期刊介绍: The Research Bulletin of Institute for Mathematical Research (MathDigest) publishes light expository articles on mathematical sciences and research abstracts. It is published twice yearly by the Institute for Mathematical Research, Universiti Putra Malaysia. MathDigest is targeted at mathematically informed general readers on research of interest to the Institute. Articles are sought by invitation to the members, visitors and friends of the Institute. MathDigest also includes abstracts of thesis by postgraduate students of the Institute.
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