Rabenstein R, Steffen P (2011)
Publication Language: English
Publication Status: Published
Publication Type: Conference contribution, Conference Contribution
Publication year: 2011
Article Number: 6076864
ISBN: 9781612848167
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.
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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