@Article{IJNAM-14-842,
author = {Krzysztof Bartosz},
title = {Variable Time-Step θ-Scheme for Nonlinear Second Order Evolution Inclusion},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2017},
volume = {14},
number = {6},
pages = {842--868},
abstract = {<p style="text-align: justify;">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 $\theta$-scheme with $\theta \in [\frac{1}{2}, 1]$, 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.</p>},
issn = {2617-8710},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/ijnam/10483.html}
}