Numerics for hyperbolic partial differential equations (PDE) via Cellular Neural Networks (CNN)

Abstract

The paper proposes an Artificial Intelligence approach for computing an approximate solution for a hyperbolic partial differential equation (PDE) modeling the vibration of a drilling plant. The basic idea relies on using the repetitive structure induced by the Method of Lines for assigning a Cellular Neural Network (CNN) to perform the numerics. The method ensures from the beginning the convergence of the approximation and preserves the stability of the initial problem.