Strict stability of high-order compact implicit finite-difference schemes: The role of boundary conditions for hyperbolic PDEs, I
Strict stability of high-order compact implicit finite-difference schemes: The role of boundary conditions for hyperbolic PDEs, I
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DOI：
10.1006/jcph.2000.6420
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发表时间：
2000-05-01
影响因子：
4.1
通讯作者：
Chertock, AE
中科院分区：
文献类型：
--
作者：
Abarbanel, SS;Chertock, AE
时间，或“严格”稳定的近似偏微分方程是更难以实现比“经典”的拉克斯稳定。本文对一维和二维双曲型初边值问题提出了一类具有严格稳定性的有限差分格式。构造的近似使得相应微分矩阵的所有特征值都有非正的真实的部分。边界条件是通过使用惩罚类条款。四阶和六阶紧致隐式有限差分格式的构造和分析。在1-D和2-D标量问题的一系列数值试验证实了该方法的计算效率。(C)北京大学出版社.
Temporal, or "strict" stability of approximation to PDEs is much more difficult to achieve than the "classical" Lax stability. In this paper, we present a class of finite-difference schemes for hyperbolic initial boundary value problems in one and two space dimensions that possess the property of strict stability. The approximations are constructed so that all eigenvalues of corresponding differentiation matrix have a nonpositive real part. Boundary conditions are imposed by using penalty-like terms. Fourth- and sixth-order compact implicit finite-difference schemes are constructed and analyzed. Computational efficacy of the approach is corroborated by a series of numerical tests in 1-D and 2-D scalar problems. (C) 2000 Academic Press.