Strict Stability of High-Order Compact Implicit Finite-Difference Schemes: The Role of Boundary Conditions for Hyperbolic PDEs, I

被引：52

作者：

Abarbanel, Saul S. ^{[1
]}

Chertock, Alina E. ^{[1
]}

机构：

[1] Department of Applied Mathematics, School of Mathematical Sciences, Tel-Aviv University, Tel-Aviv, Israel

来源：

Journal of Computational Physics | 2000年 / 160卷 / 01期

关键词：

Eigenvalues and eigenfunctions - Error analysis - Finite difference method - Initial value problems - Stability;

D O I：

10.1006/jcph.2000.6420

中图分类号：

学科分类号：

摘要：

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. © 2000 Academic Press.

引用

页码：42 / 66