Abstract
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.
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Saint-Pierre, P. Approximation of slow solutions to differential inclusions. Appl Math Optim 22, 311–330 (1990). https://doi.org/10.1007/BF01447333
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DOI: https://doi.org/10.1007/BF01447333