A Fully Spectral Method for Hyperbolic Equations

Abstract

SUMMARYThis investigation presents a fully spectral method for solving coupled hyperbolic partial differential equations. The spectral method is based on the Galerkin+ollocation technique. Two different preconditioners, the Preissmann and upyind schemes, are evaluated for their performance in solving the discretized equations. It has been found, for the cases considered, that the upwind scheme is a viable preconditioner for the fully spectral discretization of hyperbolic PDEs. Its performance as a preconditioner is in every way superior to that of the Preissmann scheme. It is established that the relative accuracy of different numerical solutions is reliably indicated by the root-mean-square average of their residuals obtained by the discretization. It is also established that the scheme gives much better accuracy than the finite-difference Preissmann scheme, for the same amount of computational effort, for both linear and non-linear problems.