Analysis of stability and convergence in FD simulations of the 1-D ultrasonic wave propagation

Finite difference (FD) methods are a well established tool for studying the propagation of pulses and waves in nonelementary media. In the present paper, we analyze some different FD schemes for smoothing the interface between two different media, and study their stability and convergence. d that an improper choice of interface model may lead to unstable or pseudoconvergent recurrence relationships and cause severe errors in the amplitudes of both the reflected and transmitted pulses.