Comparing certain classes of difference and finite element methods for a hyperbolic problem

The notion of the intervals per wavelength necessary to yield certain prescribed error levels per period is used to compare the computational efficiency of three classes of spatial differences combined with three time discretizations for the model problem ut = ux under periodic boundary conditions. The three classes of spatial difference schemes considered include high order (explicit) centered differences, smooth spline-Galerkin differences, and quite high order implicit centered differences. The three time discretizations include leap-frog, Crank-Nicolson, and 4th-order Pade' differencing.