An unconditionally stable approximation of a circular flexible plate described by a fourth order partial differential equation

0462241 - ÚTIA 2017 RIV PL eng C - Conference Paper (international conference)
Augusta, Petr - Cichy, B. - Galkowski, K. - Rogers, E.
An unconditionally stable approximation of a circular flexible plate described by a fourth order partial differential equation.
Proceedings of the 21st International Conference on Methods and Models in Automation & Robotics. Międzyzdroje: IEEE, 2016, s. 1039-1044. ISBN 978-1-5090-1867-3.
[The 21st International Conference on Methods and Models in Automation & Robotics Międzyzdroje, Poland, MMAR 2016. Amber Baltic Hotel, Międzyzdroje (PL), 29.08.2016-01.09.2016]
Institutional support: RVO:67985556
Keywords : Partial differential equation * unconditionally stable discretization * hexagonal grid
Subject RIV: BC - Control Systems Theory

An unconditionally stable finite difference scheme for systems whose dynamics are described by a second-order partial differential equation is developed with use of regular hexagonal grid. The scheme is motivated by the well-known Crank-Nicolson discretization which was developed for first-order systems. The stability of the finite-difference scheme is analyzed by von Neumann’s method. Using the new scheme, a discrete in time and space model of a deformable mirror is derived as the basis for control law design. The convergence of this scheme for various values of the discretization parameters is checked by numerical simulations.
Permanent Link: http://hdl.handle.net/11104/0261935