# Explicit Stencil Computation Schemes Generated by Poisson's Formula for the 2D Wave Equation

## TL;DR

This paper introduces a novel explicit stencil computation method for the 2D wave equation using Poisson's formula, polynomial interpolation, and exact integration, resulting in schemes with improved accuracy and stability.

## Contribution

It presents a new approach to generate explicit stencil schemes for the 2D wave equation based on Poisson's formula, with demonstrated stability and accuracy improvements.

## Key findings

- Constructed three explicit schemes with 5, 9, and 13 points.
- Schemes show larger stability regions than conventional methods.
- Simulation results confirm higher accuracy of the new schemes.

## Abstract

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.