  The objective of this article is to study the behavior of electromagnetic
field under X-ray diffraction by time-dependent deformed crystals. Derived
system of differential equations looks like the Takagi equations in the case of
non-stationary crystals. This is a system of multidimensional first-order
hyperbolic equations with complex time-dependent coefficients. Efficient
difference schemes based on the multicomponent modification of the alternating
direction method are proposed. The stability and convergence of devised schemes
are proved. Numerical results are shown for the case of an ideal crystal, a
crystal heated uniformly according to a linear law and a time-varying bent
crystal. Detailed numerical studies indicate the importance of consideration
even small crystal changes.
