On the efficiency of some fully discrete Galerkin methods for second-order hyperbolic equations

AbstractWe compare the efficiency (attained level of accuracy vs cost) of a class of Galerkin methods for the numerical solution of second-order hyperbolic equations. The methods are based on a smooth spline discretization of the space variables and on a class of time-stepping methods based on some rational approximations to the cosine function. The estimates of the error are based on approximate expressions of the dispersion of the numerical methods