A CNN Based Approach for Solving a Hyperbolic PDE Arising from a System of Conservation Laws - the Case of the Overhead Crane

The paper proposes a neurocomputing approach for numerical solving of a hyperbolic partial differential equation (PDE) arising from a system of conservation laws. The main idea is to combine the method of lines (transforming the mixed initial boundary value problem for PDE into a high dimensional system of ordinary differential equations (ODEs)) with a cellular neural network (CNN) optimal structure which exploits the inherent parallelism of the new problem in order to reduce the computational effort and storage. The method ensure from the beginning the convergence of the approximation and preserve the stability of the initial problem.