Scientific Computing Seminar
Abstract:
Temporal, or "strict", stability of the discrete approximations to PDEs is much more difficult to achieve than the "classical" Lax stability. In this talk, we present a class of finite-difference schemes for hyperbolic initial boundary value problems (IBVPs) that possess the property of temporal stability. The approximations are constructed so that all eigenvalues of the corresponding differentiation matrix have non-positive real part. Boundary conditions are imposed using penalty-type terms. The fourth- and sixth-order compact implicit finite-difference schemes are developed and analyzed. Computational efficacy of the approach is corroborated by a series of numerical tests.
<--- 1999 Index