  A new approach to building explicit time-marching stencil computation schemes
for the transient 2D acoustic wave equation is implemented. It is based on
using Poisson's formula and its three time level modification combined with
polynomial stencil interpolation of the solution at each time-step and exact
integration. The time-stepping algorithm consists of two explicit stencil
computation procedures: a first time-step procedure incorporating the initial
conditions and a two-step scheme for the second and next time-steps. Three
particular explicit stencil schemes (with five, nine and 13 space points) are
constructed using this approach. Their stability regions are presented.
Accuracy advantages of the new schemes in comparison with conventional
finite-difference schemes are demonstrated by simulation using an exact
benchmark solution.
