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\begin{document}
\title{
Approximation of parabolic equations\\
with functional dependence
 }
\author{ Henryk Leszczy\'nski} \date{}
\maketitle


\centerline{
Inst. of Math., Univ. of Gda\'nsk,  Poland,
%%%ul. Wita Stwosza 57, 80-952 Gda\'nsk, Poland,
E-mail: hleszcz@ksinet.univ.gda.pl}

\vspace{5ex}

\begin{abstract}
Consider the parabolic differential-functional
equation with functional dependence
\[
D_tu(t,x)\,=\,
\sum_{j,l=1}^na_{jl}(t,x)D_{x_jx_l}u(t,x) \,+\,
f\left(t,x,u_{(t,x)}\right),
\]
where the Hale-type functional $u_{(t,x)}$
reflects the dependence on the past
(deviating, retarded variables, integrals et.c.)
We discuss the question
of convergence for some approximate solutions (FDMs)
to an initial-value
problem for this equation.
\end{abstract}
\end{document}