Implicit discretization of linear partial differential equations and repetitive processes

Conference contribution
(Conference Contribution)


Publication Details

Author(s): Rabenstein R, Steffen P
Publication year: 2009
ISBN: 978-1-4244-2797-0
Language: English


Abstract


Implicit schemes are a popular approach to the discretization of linear partial differential equations by finite differences. They require to solve a linear set of equations in each time step. Since finite difference discretizations lead to a local coupling, these systems of equations are sparse and can be effectively solved by iterative procedures. Numerical procedures of this type are known in control theory as repetitive processes. They have mostly been used to describe control algorithms for processes where passes of finite length are repeated over and over. This contribution shows how the implicit discretization of partial differential equations can be cast into the framework of repetitive processes. Thus it establishes a link between yet unrelated results in numerical mathematics and control theory. © 2009 IEEE.


FAU Authors / FAU Editors

Rabenstein, Rudolf Prof. Dr.
Lehrstuhl für Multimediakommunikation und Signalverarbeitung


How to cite

APA:
Rabenstein, R., & Steffen, P. (2009). Implicit discretization of linear partial differential equations and repetitive processes. In Proceedings of the 2009 International Workshop on Multidimensional (nD) Systems, nDS 2009. Thessaloniki, GR.

MLA:
Rabenstein, Rudolf, and Peter Steffen. "Implicit discretization of linear partial differential equations and repetitive processes." Proceedings of the 2009 International Workshop on Multidimensional (nD) Systems, nDS 2009, Thessaloniki 2009.

BibTeX: 

Last updated on 2019-08-05 at 18:23