Numerical simulation of wave propagation in heterogeneous media poses some numerical difficulties at the interface in the domain where the solution appears by reflected and transmitted pulses. A nave implementation of even high order methods gives low order results. So, an efficient numerical approach should maintain the theoretical properties of waves propagating in nonsmooth media. This paper concerns the high order numerical solution of a one-way wave equation that contains interfaces in the solution domain. A sixth order finite difference method for advection wave equation is presented in which with a new modification this order of accuracy is also maintained at the discontinuity.

interface problems, high order methods, discontinuous coefficients, jump conditions.