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Approximation of slow solutions to differential inclusions

Saint-Pierre, Patrick (1990), Approximation of slow solutions to differential inclusions, Applied Mathematics and Optimization, 22, 1, p. 311-330. http://dx.doi.org/10.1007/BF01447333

Type
Article accepté pour publication ou publié
Date
1990
Journal name
Applied Mathematics and Optimization
Volume
22
Number
1
Publisher
Springer
Pages
311-330
Publication identifier
Metadata
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Author(s)
Saint-Pierre, Patrick
Abstract (EN)
To approach a viable solution of a differential inclusion, i.e., staying at any time in a closed convexK, a sufficient condition is given implying the convergence of an approximation sequence defined from the Euler or Runge-Kutta methods applied to a selection process which corresponds to the slowsolution concept. WhenK is smooth, the convergence condition is satisfied. This proves that the method is implementable on a computer for solving, for instance, differentiable equations with a noncontinuous right-hand side. Since the usual best approximation operator is difficult to implement, we introduce a class of quasi-projectors much more suitable for computation.
Subjects / Keywords
differential inclusions