NSFD scheme for acoustic propagation with the linearized Euler equations

Our goal is to construct a nonstandard finite difference (NSFD) scheme for the linearized Euler partial differential equations (PDE's) modeling acoustic propagation in one space dimension. Unlike other works on this discretization problem, we formulate it in terms of a single, second-order PDE rather than as two separate first-order equations. The important mathematical features of this scheme are discussed.