The implicit Euler scheme for one-sided Lipschitz differential inclusions

Beyn W-J, Rieger J (2010)
Discrete And Continuous Dynamical Systems. Series B 14(2): 409-428.

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Zeitschriftenaufsatz | Veröffentlicht | Englisch
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Abstract / Bemerkung
We propose a set-valued version of the implicit Euler scheme for relaxed one-sided Lipschitz differential inclusions and prove that the defining implicit inclusions have a well-defined solution. Furthermore, we give a convergence analysis based on stability theorems, which shows that the set-valued implicit Euler method inherits all favourable stability properties from the single-valued scheme. The impact of spatial discretization is discussed, a fully discretized version of the scheme is analyzed, and a numerical example is given.
Erscheinungsjahr
Zeitschriftentitel
Discrete And Continuous Dynamical Systems. Series B
Band
14
Ausgabe
2
Seite(n)
409-428
ISSN
PUB-ID

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Beyn W-J, Rieger J. The implicit Euler scheme for one-sided Lipschitz differential inclusions. Discrete And Continuous Dynamical Systems. Series B. 2010;14(2):409-428.
Beyn, W. - J., & Rieger, J. (2010). The implicit Euler scheme for one-sided Lipschitz differential inclusions. Discrete And Continuous Dynamical Systems. Series B, 14(2), 409-428. doi:10.3934/dcdsb.2010.14.409
Beyn, W. - J., and Rieger, J. (2010). The implicit Euler scheme for one-sided Lipschitz differential inclusions. Discrete And Continuous Dynamical Systems. Series B 14, 409-428.
Beyn, W.-J., & Rieger, J., 2010. The implicit Euler scheme for one-sided Lipschitz differential inclusions. Discrete And Continuous Dynamical Systems. Series B, 14(2), p 409-428.
W.-J. Beyn and J. Rieger, “The implicit Euler scheme for one-sided Lipschitz differential inclusions”, Discrete And Continuous Dynamical Systems. Series B, vol. 14, 2010, pp. 409-428.
Beyn, W.-J., Rieger, J.: The implicit Euler scheme for one-sided Lipschitz differential inclusions. Discrete And Continuous Dynamical Systems. Series B. 14, 409-428 (2010).
Beyn, Wolf-Jürgen, and Rieger, Janosch. “The implicit Euler scheme for one-sided Lipschitz differential inclusions”. Discrete And Continuous Dynamical Systems. Series B 14.2 (2010): 409-428.