EXPLICIT STENCIL COMPUTATION SCHEMES GENERATED BY POISSON'S FORMULA FOR THE 2D WAVE EQUATION

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.