An unconditionally stable finite difference scheme systems described by second order partial differential equations

0451268 - ÚTIA 2016 RIV PT eng C - Konferenční příspěvek (zahraniční konf.)
Augusta, Petr - Cichy, B. - Galkowski, K. - Rogers, E.
An unconditionally stable finite difference scheme systems described by second order partial differential equations.
Proceedings of the 2015 IEEE 9th International Workshop on Multidimensional (nD) Systems (nDS ). Vila Real: IEEE, 2015, s. 134-139. ISBN 978-1-4799-8739-9.
[The 2015 IEEE 9th International Workshop on MultiDimensional (nD) Systems (nDS) (2015). Vila Real (PT), 09.09.2015-11.09.2015]
Institucionální podpora: RVO:67985556
Klíčová slova: Discretization * implicit difference scheme * repetitive processes
Kód oboru RIV: BC - Teorie a systémy řízení

An unconditionally stable finite difference scheme for systems whose dynamics are described by a second-order partial differential equation is developed. 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 analysed 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.
Trvalý link: http://hdl.handle.net/11104/0252444