Stability analysis for implicit second order finite difference schemes

Rabenstein R, Steffen P (2011)


Publication Language: English

Publication Status: Published

Publication Type: Conference contribution, Conference Contribution

Publication year: 2011

Article Number: 6076864

Event location: Poitiers FR

ISBN: 9781612848167

DOI: 10.1109/nDS.2011.6076864

Abstract

Recent applications of iterative learning control and repetitive processes lead to implicit second order finite difference schemes which require practical stability testing. A von Neumann type stability analysis is employed to reduce the problem to a second order polynomial. The conditions under which its zeros lie within the unit circle can be recast by application of the bilinear transformation. Then the problem is reduced to a test for a Hurwitz polynomial. Its coefficients depend not only on the spatial frequency but also on parameters of the initial problem like step sizes in time and space. The admissible ranges of these parameters follow finally from simple inequalities. The method is demonstrated by examples. © 2011 IEEE.

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How to cite

APA:

Rabenstein, R., & Steffen, P. (2011). Stability analysis for implicit second order finite difference schemes. In Proceedings of the 2011 7th International Workshop on Multidimensional (nD) Systems, nDS 2011. Poitiers, FR.

MLA:

Rabenstein, Rudolf, and Peter Steffen. "Stability analysis for implicit second order finite difference schemes." Proceedings of the 2011 7th International Workshop on Multidimensional (nD) Systems, nDS 2011, Poitiers 2011.

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