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

Diagonally implicit multistage integration methods are employed for the numerical integration in time of first order hyperbolic systems arising from Chebyshev pseudospectral discretizations of the spatial derivatives in the wave equation. These methods have stage order q equal to the order p. The stage values can be utilized to recover approximations to the solution u of sufficiently high accuracy. The phenomenon of order reduction, which is present in the integration of differential systems by numerical methods of low stage order, such as explicit Runge-Kutta methods, is avoided.