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====== Benchmarking a simple PDE solver in Julia and other languages ======

Julia is an innovative new programming language that promises to revolutionize scientific computing. In a nutshell, it is

  * High-level, dynamic, and general-purpose, like Python
  * As fast as compiled C, roughly
  * Aimed squarely at numerics, with libraries and ease-of-use comparable to Matlab

Julia's main innovation is a carefully-designed type system combined with just-in-time compilation. The combination allows high-level user code to be compiled to machine-code on-the-fly.

The benchmark algorithm here is a simple time-integration of the Kuramoto-Sivashniksy equation

\begin{eqnarray*}
u_t = -u_{xx} - u_{xxxx} - u u_x
\end{eqnarray*}

on a 1d periodic domain $[0, L_x]$, with $x$ space and $t$ time, and where subscripts indicate differentiation.

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