Abstract
In the paper we study discrete approximations of singularly perturbed system in a finite dimensional space. When the right-hand side is almost upper semicontinuous with convex compact values and one-sided Lipschitz we show that the distance between the solution set of the original and the solution set of the discrete system is \(O\left(h^{\frac{1}{2}}\right)\).
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References
Deimling, K.: Multivalued Differential Equations. De Gruyter, Berlin (1992)
Donchev, T.: Functional differential inclusions with monotone right-hand side. Nonlinear analysis 16, 543–552 (1991)
Donchev, T., Dontchev, A.: Singular perturbations in infinite-dimensional control systems. SIAM J. Control Optim. 42, 1795–1812 (2003)
Donchev, T., Farkhi, E.: Stability and Euler approximations of one sided Lipschitz convex differential inclusions. SIAM J. Control Optim. 36, 780–796 (1998)
Donchev, T., Slavov, I.: Singularly perturbed functional differential inclusions. Set-Valued Analysis 3, 113–128 (1995)
Donchev, T., Slavov, I.: Averaging method for one sided Lipschitz differential inclusions with generalized solutions. SIAM J. Control Optim. 37, 1600–1613 (1999)
Dontchev, A., Donchev, T., Slavov, I.: A Tikhonov-type theorem for singularly perturbed differential inclusions. Nonlinear Analysis 26, 1547–1554 (1996)
Dontchev, A., Farkhi, E.: Error estimates for discretized differential inclusions. Computing 41, 349–358 (1989)
Filatov, O., Hapaev, M.: Averaging of Systems of Differential Inclusions (in Russian). Moskow University Press, Moskow (1998)
Gaitsgory, V.: Suboptimization of singularly perturbed control systems. SIAM J. Control Optim. 30, 1228–1249 (1992)
Grammel, G.: On the Time-Discretization of Singularly Perturbed Uncertain Systems. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds.) LSSC 2005. LNCS, vol. 3743, pp. 297–304. Springer, Heidelberg (2006)
Grammel, G.: Towards fully discretized differential inclusions. Set Valued Analysis 11, 1–8 (2003)
Grammel, G.: Singularly perturbed differential inclusions: an averaging approach. Set-Valued Analysis 4, 361–374 (1996)
Lempio, F., Veliov, V.: Discrete approximations of differential inclusions. Bayreuter Mathematische Schiften 54, 149–232 (1998)
Mordukhovich, B.: Discrete approximations and refined Euler-Lagrange conditions for differential inclusions. SIAM J. Control. Optim. 33, 882–915 (1995)
Veliov, V.: Differential inclusions with stable subinclusions. Nonlinear Analysis TMA 23, 1027–1038 (1994)
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Donchev, T., Lupulescu, V. (2007). Discrete Approximations of Singularly Perturbed Systems. In: Boyanov, T., Dimova, S., Georgiev, K., Nikolov, G. (eds) Numerical Methods and Applications. NMA 2006. Lecture Notes in Computer Science, vol 4310. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70942-8_36
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DOI: https://doi.org/10.1007/978-3-540-70942-8_36
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-70940-4
Online ISBN: 978-3-540-70942-8
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