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Variable Time-Step θ-Scheme for Nonlinear Second Order Evolution Inclusion
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@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 = {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.},
issn = {2617-8710},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/ijnam/10483.html}
}
TY - JOUR
T1 - Variable Time-Step θ-Scheme for Nonlinear Second Order Evolution Inclusion
AU - Krzysztof Bartosz
JO - International Journal of Numerical Analysis and Modeling
VL - 6
SP - 842
EP - 868
PY - 2017
DA - 2017/10
SN - 14
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/10483.html
KW - Clarke subdifferential
KW - hemivariational inequality
KW - second order inclusion
KW - time discretization
KW - numerical methods
AB - 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.
Krzysztof Bartosz. (1970). Variable Time-Step θ-Scheme for Nonlinear Second Order Evolution Inclusion.
International Journal of Numerical Analysis and Modeling. 14 (6).
842-868.
doi:
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