title: Parabolic PDEs in julia
body: <p>I am trying to solve a parabolic partial differential equation numerically using Julia, but I cannot find any accessible documentation that can help. </p>
  
  <p>Here is an example: t, x are 1 dimensional real. I want to solve for u(t,x)=[u1(t,x) u2(t,x)]; u satisfies the PDE</p>
  
  <p>du1/dt = d^2u1/dx^2 + a11(x,u) du1/dx + a12(x,u) du2/dx + c1(x,u)</p>
  
  <p>du2/dt = d^2u2/dx^2  + a21(x,u) du1/dx + a22(x,u) du2/dx + c2(x,u) </p>
  
  <p>Is it possible to do so in Julia? This type of problem is solvable using pdepe in Matlab. </p>