Guest editorial: Structural dynamical systems, discontinuity and numerical methods

摘要

This special issue is devoted to collect developments in computational and theoretical methods for Dynamical Systems, their numerical approximation and their applications. This volume has grown out of some contributions presented during SDS12-7th Workshop on Structural Dynamical System: Computational Aspects, the biannual workshop held in Capitolo-Monopoli Bari (Italy) 12aL"15 June 2012. Dynamical systems referred to in the title of the special issue indicate mathematical models for systems with time-dependent states and whose successive states are determined by a mathematical rules which can be described either by ordinary or partial differential equations and which can be adopted to predict and understand physical phenomena. Examples can be found in planetary system, electrical circuits, mechanical devices, particle systems, molecular dynamics just to cite some. Often, systems describing physical phenomena present different type of qualitative or geometric features, as for instance conservation laws, symplectic forms, symmetries, asymptotic behaviors. In many cases, dynamical systems are also non-smooth since they originate from non-smooth models: examples are mechanical systems subject to non-smooth contact laws (impacts, or Coulomb friction are the most common) and switched electrical circuits. Hence the study of structured and non-smooth dynamical systems gives rise to new issues in numerical methods for simulating and approximating the solutions of the problem under consideration.