Volume 14, Issue 6
Variable Time-Step θ-Scheme for Nonlinear Second Order Evolution Inclusion

Krzysztof Bartosz

Int. J. Numer. Anal. Mod., 14 (2017), pp. 842-868

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  • Abstract

We deal with a multivalued second order dynamical system involving a Clarke subdifferential of a locally Lipschitz functional. We apply a time discretization procedure to construct a sequence of solutions to a family of the approximate problems and show its convergence to a solution of the exact problem as the time step size vanishes. We consider a nonautonomous problem in which both the viscosity and the multivalued operators depend on time explicitly. The time discretization method we use, is the θ-scheme with θ ∈ [\frac{1}{2}, 1], thus, in particular, the Crank-Nicolson scheme and the implicit Euler scheme are included. We apply our result to a class of dynamic hemivariational inequalities.

  • History

Published online: 2017-10

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