Diagonally implicit multistage integration methods for pseudospectral solutions of the wave equation (Q1567641)

The acoustic wave equation in two spatial dimensions is discretized spatially by a pseudospectral Chebyshev method, and the temporal integration is done by a diagonally implicit multistage method introduced by \textit{J.~C. Butcher} [Appl. Numer. Math. 11, No. 5, 347-363 (1993; Zbl 0773.65046)]. The use of collocation at the Chebyshev-Gauss-Lobatto points imposes a rather severe stability constraint on the time step. The computed examples indicate, however, that for problems with smooth solutions, this difficulty may be ameliorated by the fact that low-order polynomials may suffice.