Distributed parameter system from Contact mechanics: Modelling and computational issues based on cellular neural networks paradigm

The paper deals with modelling and computational issues for a unified model from the Contact Mechanics belonging to the class of longitudinal vibrations of rods. The mathematical model is deduced by using the Calculus of Variation methods. The distributed parameter system is modelled by a mixed initial boundary value problem for hyperbolic partial differential equations with derivative boundaries. The computational issues can be viewed within the framework of the Neural mathematics. The approach is based on a procedure which combines a convergent Method of Lines with the Cellular Neural Networks paradigm in order to obtain a good approximation, preservation of the stability of the initial problem and a reduced computational effort even for approximating systems of huge dimension.