  In this paper, a multiscale approach with partially explicit time
discretization is proposed. The idea is to use a partially explicit time
scheme, considering a filtration problem in a fractured medium, where the
implicit scheme is used for nodes whose subdomains contain fractures, and the
explicit scheme is used for all others. In this way, it is possible to use a
time step that is independent of the diffusion coefficient for fractures.
Numerical results demonstrating high accuracy of calculations are presented.
