THE PSEUDOSPECTRAL METHOD FOR SOLVING DIFFERENTIAL EIGENVALUE PROBLEMS

A simple pseudospectral method is presented for the numerical solution of linear, differential eigenvalue problems. The method does not produce the spurious eigenvalues which generally occur when such problems are solved by the spectral tau method. The pseudospectral method is presented using two model problems, and the presentation contains a useful algorithm for the computation of the spectral differentiation matrices at general collocation points. Numerical results are offered for a set of benchmark problems, including the Orr-Sommerfeld equation for stability of plane Poiseuille flow between parallel plates. The results indicate that the new pseudospectral method is comparable in accuracy to the tau method. (C) 1994 Academic Press, Inc.