Strict Stability of High-Order Compact ImplicitFinite-Difference Schemes: The Role ofBoundary Conditions for Hyperbolic PDEs, I
نویسندگان
چکیده
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 finitedifference 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. Fourthand 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
منابع مشابه
Strict Stability of High-Order Compact ImplicitFinite-Difference Schemes: The Roleof Boundary Conditionsfor Hyperbolic PDEs, II
Strict Stability of High-Order Compact Implicit Finite-Difference Schemes: The Role of Boundary Conditions for Hyperbolic PDEs, II Saul S. Abarbanel,∗,† Alina E. Chertock,∗,‡ and Amir Yefet§ ∗Department of Applied Mathematics, School of Mathematical Sciences, Tel-Aviv University, Tel-Aviv, Israel; and §Department of Mathematical Sciences, New Jersey Institute of Technology, University Heights, ...
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