Lax-stability of fully discrete spectral methods via stability regions and pseudo-eigenvalues (Q1175225)

In the analysis of the stability for spectral methods \(\varepsilon\)- pseudo-eigenvalues are used to describe the stability region and to give necessary and sufficient conditions for Lax-stability. Examples are given where pseudo-eigenvalues differ markedly from the eigenvalues of the spatial discretization operators. In a particular example is it shown that the condition \(k=O(N^{-2})\) is both necessary and sufficient for Lax stability although the eigenvalue analysis would suggest a much weaker restriction of the form \(k\leq CN^{-1}\).