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 two-dimensional 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 5, 9, and 13 space points) are constructed using this approach. Their stability regions are presented. All of the obtained first time-step computation expressions are different from those used in conventional finite-difference methods. Accuracy advantages of the new schemes in comparison with conventional finite-difference schemes are demonstrated by simulation using an exact benchmark solution.