%  a

\documentstyle[12pt]{article}
%\setlength{\parindent}{5mm}
% \renewcommand{\baselinestretch}{1.5}
\setlength{\headheight}{0pt}
 \setlength{\headsep}{0pt}
\setlength{\footskip}{45pt}
 \setlength{\footheight}{0pt}
 \setlength{\textwidth}{430pt}
 %d%
 % \setlength{\textheight}{250pt}
 %%  \setlength{\textheight}{350pt}
%%%%%%  \setlength{\textheight}{450pt}
 %vp%
 \setlength{\textheight}{600pt}
 \setlength{\oddsidemargin}{10pt}
 \def\ha{\mbox{$\frac{1}{2}$}}
\def\be{\begin{equation}}
\def\ee{\end{equation}}
\def\ba{\begin{array}{c}}
\def\ea{\end{array}}
\def\p{\partial}
\def\ben{\[}
\def\een{\]}
\begin{document}


The functional-differential equations emerge in the analysis of the
time-dependence of systems with memory where the form and role of the
time-delay influence may vary. In the introductory-level paper, the author
considers an elementary Runge-Kutta-type discretization of the model and an
interpolation of (m steps of) its pre-history (using splines and m=4) which
reduce her equations to the tridiagonal matrix inversion problem with a
non-linearity hidden in its right-hand side. The solutions are being sought by
iterations and their convergence is analyzed. Attention is  paid to the
influence of the elimination of the linear component (changing the tridiagonal
matrix) and to the shooting method. A few numerical experiments are added using
MATLAB software.

MR2003675 Onegova, O. V. Some methods for the numerical solution of a boundary
value problem for functional-differential equations. (Russian) Izv. Ural. Gos.
Univ. Mat. Mekh. No. 4(22), (2002), 114--128.

\end{document}