Stability of a Chebychev pseudospectral solution of the wave equation with absorbing boundaries
As it is known the continuous one-dimensional problem with one absorbing boundary and one Dirichlet boundary has been shown to be far from normal and the spectrum of that problem says little about the stability behavior of the solution. In this paper, the presented analysis proves that the discrete formulation with Dirichlet boundaries at all boundaries is nearly normal. The near-normality follows from the near-normality of the second-order derivative pseudospectral differential operator. Numerical results confirm the predicted values on allowable timesteps obtained from a spectral analysis, for both Chebyshev and modified-Chebyshev implementations.
scientific article; zbMATH DE number 1121352
scientific article