Fourth-Order and Optimised Finite Difference Schemes for the 2-D Wave Equation
This paper investigates some fourth-order accurate explicit finite difference schemes for the 2-D wave equation obtained using 13-, 17-, 21-, and 25-point discrete Laplacians. Optimisation is conducted in order to minimise numerical dispersion and computational costs. New schemes are presented that are more computationally efficient than nine-point explicit schemes at maintaining less than one percent wave speed error up to some critical frequency. Simulation results are presented.