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Error estimates for discretized differential inclusions

Eine Fehlerabschätzung für diskretisierte Differentialeinschließungen

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Abstract

We present an estimate for the Hausdorff distance between the set of solutions of a differential inclusion and the set of solutions of its Euler discrete approximation, using an averaged modulus of continuity for multifunctions. A computational procedure to obtain a certain solution of the discretized inclusion is proposed.

Zusammenfassung

Eine Abschätzung der Hausdorff-Distanz zwischen der Menge aller Lösungen einer Differentialeinschließung und der Eulerschen Approximation dieser Einschließung wird vorgelegt, wobei ein Stetigkeitsmodul für Multifunktionen angewendet wird. Eine numerische Prozedur zur Auffindung einer gewissen Lösung der diskretisierten Einschließung wird vorgeschlagen.

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Authors and Affiliations

  1. Institute of Mathematics with Computer Centre Bulgarian Academy of Sciences, ul. G. Bonchev 8, 1113, Sovia, Bulgaria

    A. L. Dontchev &  E. M. Farkhi

Authors
  1. A. L. Dontchev
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  2. E. M. Farkhi
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Additional information

This work is partially supported by the Committee of Science under Grant 127.

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Dontchev, A.L., Farkhi, E.M. Error estimates for discretized differential inclusions. Computing 41, 349–358 (1989). https://doi.org/10.1007/BF02241223

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  • DOI: https://doi.org/10.1007/BF02241223

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