Stability of Pseudospectral Approximations of 1d Hyperbolic Problems
Abstract
We consider pseudospectral discretizations of the one-way wave
equation and provide a sufficient condition for asymptotic stability
of the resulting scheme which generalizes previous work by Gottlieb.
When this condition is not satisfied however we introduce a modification
of the scheme which leads again to stability and improves long term
stability of schemes which were already stable.
These ideas are also applied to 1D second-order hyperbolic
problems with first-order absorbing boundary conditions and possible
extensions to higher dimensions are discussed.
This is joined work with Z. Jackiewicz, Dept. Math..
