Abstract
In , we consider a self-adjoint matrix strongly elliptic second-order differential operator
with periodic coefficients depending on
. We find approximations of the exponential
,
, for small ε in the (
)-operator norm with suitable s. The sharpness of the error estimates with respect to τ is discussed. The results are applied to study the behavior of the solution
of the Cauchy problem for the Schrödinger-type equation
.
2010 Mathematics Subject Classification:
Acknowledgements
The author is grateful to T. A. Suslina for helpful discussions and advices.
Disclosure statement
No potential conflict of interest was reported by the author.