Time step n-tupling for wave equations

We have constructed novel temporal discretizations for wave equations. We first select an explicit time integrator that is of second order, leading to classic time marching schemes in which the next value of the wavefield at the discrete time t+Delta t is computed from current values known at time t and the previous time t-Delta t. Then, we determine how the time step can be doubled, tripled, or generally, n-tupled, producing a new time-stepping method in which the next value of the wavefield at the discrete time t thorn n Delta t is computed from current values known at time t and the previous time t-n Delta t. In-between time values of the wavefield are eliminated. Using the Fourier method to calculate space derivatives, the new time integrators allow larger stable time steps than traditional time integrators; however, like the Lax-Wendroff procedure, they require more computational effort per time step. Because the new schemes are developed from the classic second-order time-stepping scheme, they will have the same properties, except the Courant-Friedrichs-Lewy stability condition, which becomes relaxed by the factor n compared with the classic scheme. As an example, we determine the method for solving scalar wave propagation in which doubling the time step is 15% faster than a Lax-Wendroff correction scheme of the same spatial order because it can increase the time step by root 3 only.