Is there a better way to put points between a set of equations as follow:
\begin{equation}
\begin{split}
&y_1=y_0+hf_0\\
&y_2=y_0+2hf_1\\
.\\
.\\
.\\
&y_n=y_{n-1}+2hf_{n-1}
\end{split}
\label{eq: stoer method 2}
\end{equation}
The mathtools package offers the macros \vdotswithin and \shortvdotswithin for just this purpose.

\documentclass{article}
\usepackage{mathtools}
\usepackage{lmodern}
\setlength\textwidth{3in} % just for this example
\begin{document}
\begin{equation}
\begin{split}
y_1&=y_0+hf_0\\
y_2&=y_0+2hf_1\\
&\vdotswithin{=}\\ %% note the "\\" row terminator
y_m&=y_{m-1}+2hf_{m-1}\\
\shortvdotswithin{=} %% note: no row terminator
y_n&=y_{n-1}+2hf_{n-1}
\end{split}
\label{eq: stoer method 2}
\end{equation}
\end{document}
Try
\begin{equation}
\begin{split}
&y_1=y_0+hf_0\\
&y_2=y_0+2hf_1\\
\vdots\\
&y_n=y_{n-1}+2hf_{n-1}
\end{split}
\label{eq: stoer method 2}
\end{equation}
Related question about the alignment of the vertical dots that you might want to look into: Centering \vdots in a system of many equations
\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{equation}
\begin{split}
&y_1=y_0+hf_0\\
&y_2=y_0+2hf_1\\
&\vdots\\
&y_n=y_{n-1}+2hf_{n-1}
\end{split}
\label{eq: stoer method 2}
\end{equation}
But rather
\begin{equation}
\begin{array}{l}
y_1=y_0+hf_0\\
y_2=y_0+2hf_1\\
\multicolumn{1}{c}{\vdots}\\
y_n=y_{n-1}+2hf_{n-1}
\end{array}
\end{equation}
\end{document}

Certainly, the position of vertical dots can be changed.
&alignment points in asplitenvironment: It's preferable to align the rows on a common element such as=instead of on the first character of each row. While the widths ofy_1,y_2, andy_nhappen to be fairly similar, the appearance of the system of equations risks becoming marred if you also have entries such asy_[m-1}to the left of the=symbol. – Mico Jun 24 '14 at 08:57