Using subequations without amsmath

Question

Following on from my previous question regarding the use of align and aligned without 'amsmath', I am currently working on a proceedings paper, and have realised after finishing it that only specific packages are permitted - one of which is not amsmath. As a result, many of the nice equations that I have written can now no longer be built. To save me switching back to \begin{cases} \end{cases} and giving up, I thought I would try asking on here to see if anyone could provide me with a solution? My issue is now with subequations, I will provide a working example below.

I cannot define any new commands before \begin{document}, so everything must be done after that point (these are as per the MWE). I thought about trying to grab the relevant components from the style file, but to be perfectly honest I am not a TeX-wizard and have no idea whether this would even work.Could anyone provide me with a work-around, so that I can still use subequations, but by doing so after \begin{document}?

An MWE is as follows:

\documentclass{svmult}
\usepackage{mathptmx}
\usepackage{helvet}
\usepackage{courier}
\usepackage{type1cm}

\usepackage{graphicx}

\usepackage[bottom]{footmisc}

\usepackage{amssymb}
\usepackage{amsfonts}
\usepackage{amsbsy}
\usepackage{amscd}
\usepackage{amstext}
\usepackage{dsfont}
\usepackage[english]{babel}
\usepackage{color}
\usepackage{graphics}
\usepackage{epsfig}
\usepackage{subfigure}
\usepackage{wrapfig}
\usepackage{psfrag}
\usepackage{color}
\usepackage{url}
\usepackage{verbatim}
\usepackage{algorithm}
\usepackage{algorithmic}

\begin{document}

\begin{subequations}
\label{DD}
\begin{align}
&\begin{cases}
\begin{aligned}
-\Delta e_{i}^1 +  c_1 &= f_i  \quad & &\text{in} \,\, \Omega_i \\ e_{i}^1 &= 0 \quad & &\text{on} \,\, \partial\Omega_i \end{aligned}
\label{DD1}
\end{cases}
\\
&\begin{cases}
\label{DD2}
\begin{aligned}
\displaystyle\sum_{i=1}^N  \mathbf{n}_i \cdot r^1 &= - \displaystyle\sum_{i=1}^N\mathbf{n}_i \cdot r^2 \,\, & &\textrm{on} \,\, \Gamma \end{aligned}
\end{cases}
\\
&\begin{cases}
\label{DD3}
begin{aligned}
-\Delta e_{i}^2 + c_2 &= 0  \quad & &\text{in} \,\, \Omega_i \\
e_{i}^2 &= 0 \quad & &\text{on} \,\, \partial\Omega_i.  \end{aligned}
\end{cases}
\end{align}
\end{subequations}

\end{document}

Answer 1

Updated version adjusting spacing and labels, showing amsmath on the right and this code on the left

\documentclass{article}   
\usepackage{mathptmx}       
\usepackage{helvet}         
\usepackage{courier}        
\usepackage{type1cm}        

\usepackage{graphicx}        

\usepackage[bottom]{footmisc}
%\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{amsfonts}
\usepackage{amsbsy}
\usepackage{amscd}
\usepackage{amstext}
\usepackage{dsfont}
\usepackage[english]{babel}
\usepackage{color}
\usepackage{graphics}
\usepackage{epsfig}
\usepackage{subfigure}
\usepackage{wrapfig}
\usepackage{psfrag}
\usepackage{color}
\usepackage{url}
\usepackage{verbatim}
\usepackage{algorithm}
\usepackage{algorithmic}


\begin{document}

\ifx\aligned\undefined

\makeatletter
\def\aligned{{\ifnum0=`}\fi\vcenter\bgroup\let\\\cr
\halign\bgroup&\hfil$\displaystyle{}##{}$&$\displaystyle{}##{}$\hfil\cr}
\def\endaligned{\crcr\egroup\egroup\ifnum0=`{\fi}}

\def\align{\par
\bigskip
{\ifnum0=`}\fi
\let\\\cr
\halign to \textwidth\bgroup
\refstepcounter{equation}%
\global\let\@alignlab\@currentlabel
\vrule \@height \dimexpr\ht\strutbox+3pt\relax
       \@depth  \dimexpr\dp\strutbox+1pt\relax
       \@width \z@
\hbox to \textwidth{\hfill(\theequation)}\kern-\textwidth
\tabskip\fill
\hfil$\displaystyle{}##{}$&%
\let\@currentlabel\@alignlab$\displaystyle{}##{}$\hfil&%
\let\@currentlabel\@alignlab\hfil$\displaystyle{}##{}$&%
\let\@currentlabel\@alignlab$\displaystyle{}##{}$\hfil\cr}
\def\endalign{\crcr\egroup\ifnum0=`{\fi}\par\bigskip}

\newcounter{parentequation}
\newenvironment{subequations}{%
  \refstepcounter{equation}%
  \edef\theparentequation{\theequation}%
  \setcounter{parentequation}{\value{equation}}%
  \setcounter{equation}{0}%
  \def\theequation{\theparentequation\alph{equation}}%
  \ignorespaces
}{%
  \setcounter{equation}{\value{parentequation}}%
  \ignorespacesafterend
}


\def\cases{{\ifnum0=`}\fi\left\{\array{lll}}
\def\endcases{\endarray\right.\ifnum0=`{\fi}}

\makeatother
\fi



\begin{subequations}
\label{DD}
\begin{align}
&\begin{cases}
\begin{aligned}
-\Delta e_{i}^1 +  c_1 &= f_i  \quad & &\text{in} \,\, \Omega_i \\ e_{i}^1 &= 0 \quad & &\text{on} \,\, \partial\Omega_i \end{aligned}
\label{DD1}
\end{cases}
\\
&\begin{cases}
\label{DD2}
\begin{aligned}
\displaystyle\sum_{i=1}^N  \mathbf{n}_i \cdot r^1 &= - \displaystyle\sum_{i=1}^N\mathbf{n}_i \cdot r^2 \,\, & &\textrm{on} \,\, \Gamma \end{aligned}
\end{cases}
\\
&\begin{cases}
\label{DD3}
\begin{aligned}
-\Delta e_{i}^2 + c_2 &= 0  \quad & &\text{in} \,\, \Omega_i \\
e_{i}^2 &= 0 \quad & &\text{on} \,\, \partial\Omega_i.  \end{aligned}
\end{cases}
\end{align}
\end{subequations}



\begin{equation}
\label{InitSystemNL}
\left\{
\begin{aligned}
\mathcal{R} \colon= -\Delta u &= f  \quad & &\text{in} \,\, \Omega \\ u &= 0 \quad & &\text{on} \,\, \partial\Omega, 
\end{aligned} 
\right.
\end{equation}


[\ref{DD}][\ref{DD3}]
\end{document}