break a long equation with an initial bracket

Question

I tried to fix this problem by reading the answers to the questions on this forum related to this topic, but I did not find any solution. Could you help me, please? The thing is that I have to break a long equation with an initial bracket...Because of that, I am not able to use neither split nor align...Here the text

\begin{equation}
u_{i}^{n+1} = \frac{1}{2} \hat u_m^n e^{Ii\phi_m} \left\{ \frac{1}{2} \left(e^{I\phi_m}+e^{-I\phi_m}+2\right) 
-\frac{\Gamma}{2} \left(e^{I\phi_m} + e^{-I\phi_m}\right) - \Gamma \left[ \frac{1}{2} \left(e^{I\phi_m} + e^{-I\phi_m}\right) - \frac{\Gamma}{2} \left(e^{I\phi_m} + e^{-I\phi_m} -2\right)\right] \right\}. \notag
\end{equation}

Answer 1

It seems that the terms in your equation have the same height. This means that TeX can estimate the braces height from any of them. Therefore the construction

 \left\{ ....  \right.\\
 \left.  ....  \right\}

works right (otherwise we would need to put the delimiter sizes explicitly or to use \vphantom{THE_HIGHEST_TERM} in the corresponding line).

This works:

\documentclass{article}
\usepackage{amsmath}
\pagestyle{empty}
\begin{document}

\begin{multline}
u_{i}^{n+1} = \frac{1}{2} \hat u_m^n e^{Ii\phi_m} \left\{ \frac{1}{2}
  \left(e^{I\phi_m}+e^{-I\phi_m}+2\right)  
  -\frac{\Gamma}{2} \left(e^{I\phi_m} + e^{-I\phi_m}\right) - 
  \right.\\
  \left.
   \Gamma \left[ \frac{1}{2} \left(e^{I\phi_m} + e^{-I\phi_m}\right) -
   \frac{\Gamma}{2} \left(e^{I\phi_m} + e^{-I\phi_m} -2\right)\right]
\right\}. \notag 
\end{multline}

\end{document}