Loading [MathJax]/extensions/TeX/boldsymbol.js
\newcommand{\uex}{{u_{\small\mbox{e}}}}
\newcommand{\Aex}{{A_{\small\mbox{e}}}}
\newcommand{\half}{\frac{1}{2}}
\newcommand{\tp}{\thinspace .}
\newcommand{\Oof}[1]{\mathcal{O}(#1)}
\newcommand{\dfc}{\alpha} % diffusion coefficient
Example
Test problem:
\begin{align*}
u_t &= u_{xx},\quad &x\in (0,1),\ t\in (0,T]\\
u(0,t) &= u(1,t) = 0,\quad &t\in (0,T]\\
u(x,0) & = \sin (\pi x) + 0.1\sin(100\pi x)
\end{align*}
Exact solution:
u(x,t) = e^{-\pi^2 t}\sin (\pi x) + 0.1e^{-\pi^2 10^4 t}\sin (100\pi x)
